Related papers: Soliton solutions for Q3
In this paper, we study the Cauchy problem for the focusing nonlinear short-pluse equation by using $\overline\partial$ steepest descent method. \begin{align} &u_{xt}=u+\frac{1}{6}(u^3)_{xx}, \nonumber\\ &u(x,0)=u_0(x)\in…
This paper investigates the algebraic reduction of the infinite-dimensional symmetries of the Ablowitz-Kaup-Newell-Segur system when restricted to multi-soliton solution. By systematically analyzing, we demonstrate that the entire…
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized…
We investigate certain $Z_3$-graded associative algebras with cubic $Z_3$-invariant constitutive relations. The invariant forms on finite algebras of this type are given in the low dimensional cases with two or three generators. We show how…
In this work, the $\overline{\partial}$ steepest descent method is employed to investigate the soliton resolution for the Hirota equation with the initial value belong to weighted Sobolev space $H^{1,1}(\mathbb{R})=\{f\in L^{2}(\mathbb{R}):…
We construct various types of degenerate multi-soliton and multi-breather solutions for the sine-Gordon equation based on B\"{a}cklund transformations, Darboux-Crum transformations and Hirota's direct method. We compare the different…
Recent work of Harland shows that the $SO(3)$-symmetric, dimensionally-reduced, charge-$N$ self-dual Yang--Mills calorons on the hyperbolic space $ H^3\times S^1$ may be obtained through constructing $N$-vortex solutions of an Abelian Higgs…
In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirota equation and give its explicit form. Unlike the previous…
The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for…
In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of…
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these…
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed…
It is well known that, for even n, the n-soliton solution on the Minkowski seed, constructed using the inverse-scattering method (ISM) of Belinski and Zakharov (BZ), is the multi-Kerr-NUT solution. We show that, for odd n, the natural seed…
We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the…
We discuss some properties of the soliton equations of the type, partial derivative u/partial derivative t = S [u, (u) over bar], where S is a nonlinear operator differential in x, and present the additivity theorems of the class of the…
An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of $N$-soliton solutions of the…
We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…
The recent investigation on various form factors of the nucleon is reviewed in the framework of the SU(3) chiral quark-soliton model. The results for the electromagnetic and scalar form factors are in remarkable agreement with experimental…
In [1], a generalized type of Darboux transformations defined in terms of a twisted derivation was constructed in a unified form. Such twisted derivations include regular derivations, difference operators, superderivatives and…
General rational solutions for the nonlocal resonant nonlinear Schrodinger equations are derived by using the Hirota bilinear method and the KP hierarchy reduction method. These rational solutions are presented in terms of determinants in…