arXiv subjects

Maria Gandarias

Publications and source records attributed to Maria Gandarias.

4 recordsLinked to original sources

arXiv2024

Weak compactons of nonlinearly dispersive KdV and KP equations

A weak formulation is devised for the K(m,n) equation which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones that do not exist as classical (strong) solutions. Similar results are obtained for a nonlinearly dispersive generalization of the gKP equation in two dimensions, which possesses line compacton solutions.

math-ph↗

arXiv2021

Symmetries, conservation laws, and generalized travelling waves for a forced Ostrovsky equation

Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation laws is presented. Generalized travelling wave solutions are obtained through symmetry reduction. These solutions exhibit a wave profile that is stationary in a moving reference frame whose speed can be constant, accelerating, or decelerating.

math-ph↗

arXiv2021

Nonlinearly dispersive KP equations with new compacton solutions

A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are given on the nonlinearity powers in this equation under which a travelling wave can be cut off to obtain a compacton. Numerous explicit examples having various profiles are derived, including a quadratic function, powers of a cosine, and powers of Jacobi $\cn$ functions, all of which are symmetric. The cosine and $\cn$ symmetric compactons have an anti-symmetric counterpart. In comparison, explicit solitary waves of the generalized KP equation are found to have profiles given by a power of a sech and a reciprocal quadratic function. Kinematic properties of all of the different types of compactons and solitary waves are discussed, along with conservation laws of the generalized KP equation.

math-ph↗

arXiv2017

Conservation laws and symmetries of time-dependent generalized KdV equations

A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries is derived. The physical meaning of the conservation laws and the symmetries is discussed.

math-ph↗