arXiv subjects

Anjan Kundu

Publications and source records attributed to Anjan Kundu.

At least 19 recordsLinked to original sources

arXiv2018

Novel nonlinear wave equation: regulated rogue waves and accelerated soliton solutions

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.

nlin.PS↗

arXiv2018

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrodinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bili- nearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathe- matical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2þ1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.

nlin.SI↗

arXiv2018

Bending of solitons in weak and slowly varying inhomogeneous plasma

Bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev- Petviashvili equation is obtained with a chosen unperturbed ion density profile. Exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, whereas the amplitude of the soliton remaining constant

physics.plasm-ph↗

arXiv2016

Controlling near shore nonlinear surging waves through bottom boundary conditions

Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.

physics.flu-dyn↗

arXiv2016

Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion and Skyrmion crystal with asymmetry, likely to be detected in precision experiments.

cond-mat.stat-mech↗

arXiv2016

Exact Bethe ansatz solution for a quantum field model of interacting scalar fields in quasi-two dimensions

Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang-Baxter integrability is proved for the model by finding a new kind of commutation rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau-Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.

nlin.SI↗

arXiv2016

Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension

Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-time concept in integrable systems and construct a novel quantum nonlinear Schroedinger model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.

hep-th↗

arXiv2015

Lagrangian and Hamiltonian structures in an integrable hierarchy and space-time duality

We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a {\it space} evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an $r$-matrix structure, whereas traditionally only one of them is involved in the classical $r$-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.

math-ph↗

arXiv2015

Asymmetric Skyrmion lattice in helimagnets

Intricate spin textures in helimagnets, identified as stable topological Skyrmions, were observed experimentally, where Skyrme lattice was supposed to exhibit symmetric structures in the ground state. We show the possibility of asymmetric Skyrmions in a helimagnetic model, for individual Skyrmion as well as for the hexagonal Skyrme crystal with higher charge, as perturbative deformation and stabilization of exact ferromagnetic solitons. Such nonsymmetric configurations for the Skyrme lattice, predicted here theoretically, need to be verified in precision experiments.

cond-mat.str-el↗

arXiv2015

Arbitrary bending of optical solitonic beam regulated by boundary excitations in a doped resonant medium

Bending of a shape-invariant optical beam is achieved so far along parabolic or circular curves. Borrowing ideas used in nonlinear optical communication, we propose such a bending along any preassigned curve or surface, controlled by the boundary population inversion of atoms in an Erbium doped medium. The optical beam generated in a nonlinear Kerr medium and transmitted through a doped resonant medium as an accelerating soliton predicted here, should be realizable experimentally and applicable to nonlinear events in other areas like plasma or ocean wave.

nlin.PS↗

arXiv2015

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the Rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension(1D) with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose a two-dimensional(2D), exactly solvable Nonlinear Schrödinger equation(NLS), derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed 2D equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The 2D NLS equation allows also an exact lump solution which can model a full grown surface Rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appear and disappear preceded by a hole state, with its dynamics controlled by the current term.These desirable properties make our exact model promising for describing ocean rogue waves.

nlin.SI↗

arXiv2013

Novel integrable higher-dimensional nonlinear Schroedinger equation: properties, solutions, applications

An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its connection with other known models like the Zakharov equation and the Strachan construction is shown. The underlying integrable structures like the Lax pair, the infinite conserved charges and the higher soliton solutions are presented in the explicit form. The related 2D rogue wave model and other applications are focused on.

nlin.SI↗

arXiv2012

Unraveling hidden hierarchies and dual structures in an integrable field model

An integrable field theory, due to path-independence on the space-time plane, should yield together with an infinite set of independent conserved charges also similar dual charges determining the boundary and defect contributions. On the example of the nonlinear Schroedinger equation we unravel hidden hierarchies and dual structures and show the complete integrability through a novel Yang-Baxter equation at the classical and quantum level with exact solution.

nlin.SI↗

arXiv2011

Hidden possibilities in controlling optical soliton in fiber guided doped resonant medium

Fiber guided optical signal propagating in a Erbium doped nonlinear resonant medium is known to produce cleaner solitonic pulse, described by the self induced transparency (SIT) coupled to nonlinear Schroedinger equation. We discover two new possibilities hidden in its integrable structure, for amplification and control of the optical pulse. Using the variable soliton width permitted by the integrability of this model, the broadening pulse can be regulated by adjusting the initial population inversion of the opant atoms. The effect can be enhanced by another innovative application of its constrained integrable hierarchy, proposing a system of multiple SIT media. These theoretical predictions are workable analytically in details, correcting the limitation of a well known result.

nlin.SI↗

arXiv2010

Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear Schrödinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, $N$-particle sectors of which yield the well known anyon gases, interacting through $δ$ and derivative $δ$-function potentials.

nlin.SI↗

arXiv2010

Architecture and Algorithms for an Airborne Network

The U.S. Air Force currently is in the process of developing an Airborne Network (AN) to provide support to its combat aircrafts on a mission. The reliability needed for continuous operation of an AN is difficult to achieve through completely infrastructure-less mobile ad hoc networks. In this paper we first propose an architecture for an AN where airborne networking platforms (ANPs - aircrafts, UAVs and satellites) form the backbone of the AN. In this architecture, the ANPs can be viewed as mobile base stations and the combat aircrafts on a mission as mobile clients. The combat aircrafts on a mission move through a space called air corridor. The goal of the AN design is to form a backbone network with the ANPs with two properties: (i) the backbone network remains connected at all times, even though the topology of the network changes with the movement of the ANPs, and (ii) the entire 3D space of the air corridor is under radio coverage at all times by the continuously moving ANPs. In addition to proposing an architecture for an AN, the contributions of the paper include, development of an algorithm that finds the velocity and transmission range of the ANPs so that the dynamically changing backbone network remains connected at all times, development of a routing algorithm that ensures a connection between the source-destination node pair with the fewest number of path switching, given the dimensions of the air corridor and the radius of the coverage sphere associated with an ANP, development of an algorithm that finds the fewest number of ANPs required to provide complete coverage of the air corridor at all times, development of an algorithm that provides connected-coverage to the air corridor at all times, and development of a visualization tool that depicts the movement patterns of the ANPs and the resulting dynamic graph and the coverage volume of the backbone network.

cs.NI↗

arXiv2009

Two-fold integrable hierarchy of nonholonomic deformation of the DNLS and the Lenells-Fokas equation

The concept of the nonholonomic deformation formulated recently for the AKNS family is extended to the Kaup-Newell class. Applying this construction we discover a novel two-fold integrable hierarchy related to the deformed derivative nonlinear Schrödinger (DNLS) equation and found the exact soliton solutions exhibiting unusual accelerating motion for both its field and the perturbing functions. Extending the idea of deformation the integrable perturbation of the gauge related Chen-Lee-Liu DNLS equation is constructed together with its soliton solution. We show that, the recently proposed Lenells-Fokas (LF) equation falls in the deformed DNLS hierarchy, sharing the accelerating soliton and other unusual features. Higher order integrable deformations of the LF and the DNLS equations are proposed.

nlin.SI↗

arXiv2009

Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations

We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the AKNS family, e.g. for the KdV, the mKdV, the NLS and the SG equation, showing thus a two-fold universality of the recently found deformation for the KdV equation.

nlin.SI↗