Related papers: A comparison of two discrete mKdV equations
We prove the nonlinear stability of the KdV solitary waves considered as solutions of the KP-II equation, with respect to periodic transverse perturbations.
In this paper, we consider a kind of shallow water wave model called the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. We firstly consider the unperturbed KP-BBM equation. Then by using the geometric singular perturbation…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
We study a discrete Darboux transformation and construct the multi-soliton solutions in terms of ratio of determinants for integrable discrete sine-Gordon equation. We also calculate explicit expressions of single, double, triple, quad…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
The logarithmic KdV (log-KdV) equation admits global solutions in an energy space and exhibits Gaussian solitary waves. Orbital stability of Gaussian solitary waves is known to be an open problem. We address properties of solutions to the…
Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations. These links can be depicted in a…
The nonlinear wave solutions to coupled mKdV equations with variable coefficients are obtained by using the F-expansion method, including 12 kinds of Jacobi elliptic function solutions. In the limit cases, the torsional wave solutions,…
We address justification and solitary wave solutions of the cylindrical KdV equation which is formally derived as a long wave approximation of radially symmetric waves in a two-dimensional nonlinear dispersive system. For a regularized…
We consider the following hypothesis: some of KdV equation shock-like waves are invariant with respect to the combination of the Galilean symmetry and KdV equation higher symmetries. Also we demonstrate our approach on the example of…
We introduce a parametric coupled KdV system which contains, for particular values of the parameter, the complex extension of the KdV equation and one of the Hirota-Satsuma integrable systems. We obtain a generalized Gardner transformation…
We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular discrete motion of discrete planar curves.
In the context of the full line Schrodinger equation, we revisit the binary Darboux transformation (double commutation method) which inserts or removes any number of positive eigenvalues embedded into the absolutely continuous spectrum…
The present paper is a numerical study of the dynamics of solitary wave solutions of the fractional nonlinear Schr\"{o}dinger equation, whose existence was analyzed by the authors in the first part of the project. The computational study…
The paper's main goal is to compare the motion of solitary surface waves resulting from two similar but slightly different approaches. In the first approach, the numerical evolution of soliton surface waves moving over the uneven bottom is…
Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an…
The paper is devoted to analysis of different models that describe waves in fluid-filled and gas-filled elastic tubes and development of methods of calculation and numerical analysis of solutions with solitary waves and kinks for these…
We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the…
In this paper, we define the modified formal variable separation approach and show how it determines, in a remarkably simple manner, the decomposition solutions, the B\"acklund transformations, the Lax pair, and the linear superposition…
This manuscript embarks on an in-depth exploration of the modified Korteweg-de Vries (mKdV) equation, with a particular emphasis on unraveling the intricate structure of its infinite symmetries and their physical interpretations. Central to…