Related papers: Interaction properties of complex mKdV solitons
The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation. These two generalizations admit oscillatory solitons, which describe harmonically modulated complex…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision…
We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or…
The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed KdV equation, the asymptotic expansion of the solution is…
Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg-de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes.…
Interaction of two solitons of the different polarities in the framework of modified Korteweg-de Vries (mKdV) equation is studied. Three types of soliton interaction are considered: exchange and overtaking for solitons of the same polarity,…
In this paper, we are concerned with various soliton solutions to the coupled Hirota equation, as well as to the Sasa-Satsuma equation which can be viewed as one reduction case of the coupled Hirota equation. First, we derive bright-bright,…
The N=2 supersymmetric KdV equation of Inami and Kanno is bilinearized employing the Hirota method and the existence of $N$ soliton solutions is demonstrated. The exact form of the solutions are explicitly obtained and an interesting…
The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by…
We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg-de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton…
We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton…
Numerical experiments involving the interaction of two solitary waves of the ion acoustic plasma equations are described. An exact 2-soliton solution of the relevant KdV equation was fitted to the initial data, and good agreement was…
In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave-short wave resonance interaction ($M$-LSRI) system. First, we briefly revisit our…
Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…
We study the dynamics of soliton solutions to the perturbed mKdV equation $\partial_t u = \partial_x(-\partial_x^2 u -2u^3) + \epsilon V u$, where $V\in \mathcal{C}^1_b(\mathbb{R})$, $0<\epsilon\ll 1$. This type of perturbation is…
There has been found an exact solution of the mixed problem for Shrodinger's compact U(m)-vector nonlinear model with an arbitrary sign of the coupling constant. It is shown, that in case of m>2 there is a new class of solutions - mixed…
Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov…
This paper presents a complete description of the interaction of two solitons with nearly equal speeds for the quartic (gKdV) equation. By constructing an approximate solution of the problem, we prove that at the main order, the two…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…