We undertake a detailed comparison of the results of direct numerical simulations of the soliton gas dynamics for the Korteweg – de Vries equation with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. Two model problems are considered: (i) the propagation of a ‘trial’ soliton through a one-component ‘cold’ soliton gas consisting of rand...

This paper aims to seek soliton solutions for the nonlocal generalized Sasa–Satsuma (gSS) equation by constructing Darboux transformation (DT). We obtain gSS equation, including double-periodic wave, breather-like, KM-breather solution, dark-soliton, W-shaped soliton, M-shaped periodic double-peak dark-breather, bright-breather, and breather solutions. Furthermore, interaction of these solitons...

It is shown that, by letting wavenumbers and frequencies complex in Hirota’s bilinear method, new classes of exact solutions of soliton equations can be obtained systematically. They include not only singular or N -homoclinic solutions but also N -wavepacket solutions. PACS: 03.40.Kf, 47.35.+i

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived. Keywords—Hirota bilinear method, potential KadomtsevPetviashvili equation, Multiple sol...

We speculate that the universe is filled with stars composed of electromagnetic and dilaton fields. We calculate soliton-like solutions of these fields and show that their energy can be converted into a relativistic plasma in an explosive way whioch produces strong gamma-ray bursts observed in the universe. The conversion proceeds as in classical detonation theory by a relativistic self-similar...

A modified mapping method is used to obtain variable separation solutions with two arbitrary functions of the (2+1)-dimensional modified dispersive water-wave system. Based on the variable separation solution and by selecting appropriate functions, we discuss interaction behaviours among special anti-solitons constructed by multi-valued functions. The analysis results exhibit that the interacti...

The general solution is found to a bilinear reduction of the higher order nonlinear Schrödinger equation. Except for the previously known special cases having multisoliton solutions, the solution has the form of a single envelope solitary wave or wave train for all other values of the parameters. We conjecture that the generic solution is limited to such a narrow class of functions because the ...

By means of the coupled amplitude-phase method we find analytical dark solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media. The dark solitary wave solution exists even for the coefficients of quintic terms much larger than...

New analytic sech2-type traveling solitary-wave solutions, satisfying zero background at infinity, of a general fifth-order shallow water-wave model are found and compared with previously obtained non-zero background solutions. The allowed coefficient regions for the solitary-wave solutions are classified by requiring the wave number and angular frequency to be real. Detailed numerical simulati...