arXiv subjects

N. Sawado

Publications and source records attributed to N. Sawado.

At least 19 recordsLinked to original sources

arXiv2026

Compact Q-balls and Q-shells within a $CP^N$ Skyrme-Faddeev type model

While $CP^N$ models with analytic potentials are known to support finite-energy compact Q-ball and Q-shell solutions, their behavior in more complex Lagrangian frameworks remains a subject of active research. This work explores these non-topological structures within an extended Skyrme-Faddeev-type model that incorporates quartic derivative terms. In this context, harmonic time dependence and the presence of quartic terms constitute two independent stabilization mechanisms that allow the configurations to circumvent Derrick's scaling argument. We investigate the necessary conditions for the existence of these solutions and analyze the influence of quartic terms on the properties of the resulting compactons, specifically examining the $E(Q)$ relationship between energy and Noether charge. Our findings provide valuable insights into the stability and characteristics of compact boson stars within $CP^N$ models featuring higher-order derivative terms.

hep-th↗

arXiv2025

PINNs Study for the Bekki-Nozaki Chaos in the Non-linear Schrödinger equation

In this paper we study chaotic behavior in the forced dissipative non-linear Schrödinger equation, so called the Bekki-Nozaki equation. Chaotic systems are often seen in a strong sensitivity to initial conditions,leading to error accumulation over time when traditional numerical methods are applied. To address this difficulty, we employ Physics-Informed Neural Networks(PINNs), a mesh-free deep learning framework. PINNs mitigate error accumulation in chaotic systems by solving partial differential equations without discretizing the computational domain. We demonstrate that PINNs successfully reproduce chaotic behavior of the Bekki-Nozaki equation. The results of the inverse analysis indicate a correlation between the governing equation's predictability and its chaotic nature of the solution.

nlin.CD↗

arXiv2025

Inelastic Scattering, Emergent Interactions of Solitons in the Zakharov-Kuznetsov Equation through Conservative and non-Conservative Physics-Informed Neural Networks

The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system. Physics-Informed Neural Networks (PINNs) are used to study the collision of soliton solutions in the 2+1 dimensional Zakharov-Kuznetsov equation. PINNs are able to successfully solve the equations in the forward process, and the solutions are obtained using a mesh-free approach and automatic differentiation, taking into account conservation laws. In the inverse process, the proper form of the equation can be successfully derived from a given training data. However, the situation becomes intractable in the collision process. The forward analysis result no longer adheres to the laws of conservation, and is better described as a dynamically incompatible field configuration (DIFC) than a solution to the system. Conservative PINNs have thus been introduced for this purpose, and in this paper we succeed in obtaining solutions that satisfy conservation laws. The inverse analysis suggests a different equation in which the coefficients exhibit significant changes, implying an emergence of temporary interactions. With these modulated coefficients, we recalculate the equation and confirm that the adherence to the laws of conservation has unquestionably improved.

nlin.SI↗

arXiv2025

Discovery of Quasi-Integrable Equations from traveling-wave data using the Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for analyzing nonlinear partial differential equations and identifying governing equations from observational data. In this study, we apply PINNs to investigate vortex-type solutions of quasi-integrable equations in two spatial dimensions, specifically the Zakharov-Kuznetsov (ZK) and the Regularized Long-Wave (RLW) equations. These equations are toy models for geostrophic shallow water dynamics in planetary atmospheres. We first demonstrate that PINNs can successfully solve these equations in the forward process using a mesh-free approach with automatic differentiation. However, in the inverse process, substantial misidentification occurs due to the structural similarities between the ZK and the RLW equations. To address this issue, we then introduce conservation law-enhanced PINNs, initial condition variations, and a friction-based perturbation approach to improve identification accuracy. Our results show that incorporating small perturbations while preserving conservation laws significantly enhances the resolution of equation identification. These findings may contribute to the broader goal of using deep learning techniques for discovering governing equations in complex fluid dynamical systems, such as Jupiter's Great Red Spot.

physics.flu-dyn↗

arXiv2023

Gauged compact $Q$-balls and $Q$-shells in a multi-component $CP^N$ model

We study a multicomponent $CP^N$ model's scalar electrodynamics. The model contains $Q$-balls and $Q$-shells, which are nontopological compact solitons with time dependency $e^{i\omega t}$. Two coupled $CP^N$ models can decouple locally if one of their $CP^N$ fields takes the vacuum value. Because of the compacton nature of solutions, $Q$-shells can shelter another compact $Q$-ball or $Q$-shell within their hollow region. Even if compactons do not overlap, they can interact through the electromagnetic field. We investigate how the size of multicompacton formations is affected by electric charge, with a focus on structures with nonzero or zero total net charge.

hep-th↗

arXiv2022

Nodal compact $Q$-ball/$Q$-shell in the $\mathbb{C}P^N$ nonlinear sigma model

Nodal, excited compactons in the $\mathbb{C}P^N$ models with V-shaped potentials are analyzed. It is shown that the solutions exist as compact $Q$-balls and $Q$-shells. The solutions have a discontinuity in the second derivative associated with the character of the potential, however, their energy and charge densities are both continuous. The excited $Q$-balls and $Q$-shells are analyzed as electrically neutral and electrically charged objects.

hep-th↗

arXiv2021

Compact Q-balls and Q-shells in a multi-component $\mathbb{C}P^N$ model

Coupled multi-component $\mathbb{C}P^N$ models with V-shaped potentials are analyzed. It is shown that the model has solutions being combinations of compact Q-balls and Q-shells. The compact nature of solutions permits the existence of novel harbor-type solutions having the form of Q-balls sheltered by Q-shells. The relation between the energy $E$ and Noether charge $Q$ is discussed both analytically and numerically. The energy of the solutions behaves as $E\sim |Q|^α,~α<1$, i.e., as for the standard Q-ball. Furthermore, the ratio $E/Q$ for various configurations in the multi-component model suggests that the solutions are at least classically stable.

hep-th↗

arXiv2019

Creating Oscillons and Oscillating Kinks in Two Scalar Field Theories

Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in $1 + 1$ spatiotemporal dimensions. The solutions contain a control parameter, the variation of which produces oscillons and kinks with a flat-top shape. The model finds applications to condensed matter, cosmology, and high-energy physics.

hep-th↗

arXiv2014

Dirac equation for sphercially symmetric $AdS_5$ space-time and application to a boson star in EGB gravity

We discuss the Dirac equation in a curved 5-dimensional spherically symmetric space-time. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating space-times with equal angular momenta. It has a symmetry $SU(2)\times U(1)$ and is implemented by the Wigner functions. The radial part forms a Dirac-Schrödinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein-Gauss-Bonnet space-time and the space-time of a boson star.

gr-qc↗

arXiv2012

Numerical vortex solutions in (3+1) dimensions for the extended $CP^N$ Skyrme-Faddeev model

We construct numerical vortex solutions in a (3+1) dimensional Minkowski space-time for the extended version of the Skyrme-Faddeev model with target space $CP^N$. The solutions are essentially composed of $N$-th single vortex which does not belong to the integrable sector. They have finite energy per unit length and contain waves propagating along vortices with the speed of light. In this Letter we report on the case N=2 and show existence of the solutions with the charges $(n_1,n_2)=(1,2)$.

hep-th↗

arXiv2012

Some vortex solutions in the extended Skyrme-Faddeev model

Analytical and numerical vortex solutions for the extended Skyrme-Faddeev model in a (3+1) dimensional Minkowski space-time are investigated. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the SO(3) symmetry down to SO(2). The construction of the solutions has been done in twofold: one makes use of an axially symmetric ansatz and solves the resulting ODE by an analytical and a numerical way. The analytical vortices are obtained for special form of the potentials, and the numerical ones are computed using the successive over relaxation method for wider choice of the potentials. Another is based on a simulational technique named the simulated annealing method which is available to treat the non-axisymmetric shape of solutions. The crucial thing for determining the structure of vortices is the type of the potential.

hep-th↗

arXiv2008

SU(3) dibaryons in the Einstein-Skyrme model

SU(3) collective coordinate quantization to the regular solution of the B=2 axially symmetric Einstein-Skyrme system is performed. For the symmetry breaking term, a perturbative treatment as well as the exact diagonalization method called Yabu-Ando approach are used. The effect of the gravity on the mass spectra of the SU(3) dibaryons and the symmetry breaking term is studied in detail. In the strong gravity limit, the symmetry breaking term significantly reduces and exact SU(3) flavor symmetry is recovered.

hep-th↗

arXiv2006

Nuclear matter in the chiral quark soliton model with vector mesons

We study the nuclear matter solution in the chiral quark soliton model coupled to $ρ$ and $ω$ vector mesons based on the Wigner-Seitz approximation. It is shown that the vector mesons stabilize the soliton at high-density region. As a result, the saturation property and incompressibility are significantly improved.

hep-ph↗

arXiv2005

Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $σ$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes the soliton solution. In this paper we derive an extended action including second derivative terms and obtain soliton solutions numerically. A new topological lower bound formula is infered for the extended action.

hep-ph↗

arXiv2005

Quantization of the chiral soliton in medium

Chiral solitons coupled with quarks in medium are studied based on the Wigner-Seitz approximation. The chiral quark soliton model is used to obtain the classical soliton solutions. To investigate nucleon and $Δ$ in matter, the semi-classical quantization is performed by the cranking method. The saturation for nucleon matter and $Δ$ matter are observed.

hep-ph↗

arXiv2005

Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $σ$ model in three dimensional space upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the thoery contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second derivative term perturbatively and show that the SFN model with the second derivative term possesses soliton solutions.

hep-ph↗

arXiv2003

Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model

In this paper, we study axially symmetric solutions with $B=2-5$ in the chiral quark soliton model.In the background of axially symmetric chiral fields, the quark eigenstates and profile functions of the chiral fields are computed self-consistently. The resultant quark bound spectrum are doubly degenerate due to the symmetry of the chiral field. Upon quantization, various observable spectra of the chiral solitons are obtained. Taking account of the Finkelstein-Rubinstein constraints, we show that our results exactly coincide with the physical observations for B=2 and 4 while B=3 and 5 do not.

hep-ph↗

arXiv2002

Search for the quark shell structure using the non-topological soliton model

We investigate higher baryon-number states in the Chiral Quark Soliton Model using the rational map ansatz for the background chiral fields. The soliton solutions are obtained self-consistently. We show that the baryon number density has point-like symmetries and the corresponding valence quark spectrum of the lowest energy exhibits approximate four-fold degenerate. Our results indicate the possibility of existence of the shell-like structure in the multi-baryonic system.

hep-ph↗