相关论文: Hirota's virtual multi-soliton solutions of N=2 su…

We construct several new integrable systems corresponding to nonlocal versions of the Hirota equation, which is a particular example of higher order nonlinear Schr\"{o}dinger equations. The integrability of the new models is established by…

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger…

The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be…

The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its soliton solutions are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these…

Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified…

In a previous work[1] exact stable oblique soliton solutions were revealed in two dimensional nonlinear Schroedinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt…

Synchronous collisions of solitons of the Korteweg -- de Vries equation are considered as a representative example of the interaction of a large number of solitons in a soliton gas. Statistical properties of the soliton field are examined…

Employing the Lax pairs of the noncommutative discrete potential Korteweg--de Vries (KdV) and Hirota's KdV equations, we derive differential--difference equations that are consistent with these systems and serve as their generalised…

Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides…

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…

We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this superequation yields the system of new nonlocal variables…

The N-cnoidal solution of the Korteweg-de Vries (KdV) evolution equation is presented based on the prolongation structure theory of Wahlquist and Estabrook [J. Math. Phys. \textbf{16}, 1 (1975)]. The generalized KdV cnoidal wave solutions…

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…

Within the framework of the Inverse-Scattering formalism and the Hirota algorithm, soliton solutions of evolution equations are images of {\tau}-functions. Typically, the latter are expressed in terms of exponentials, the arguments of which…

In this paper we consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota-Ohta system. The Lax pair of the Hirota-Ohta system was extended to a Lax triad by adding extra third linear equation, whose…

We study pointwise spatial decay of multi-solitons of the generalized Korteweg-de Vries equations. We obtain that, uniformly in time, these solutions and their derivatives decay exponentially in space on the left of and in the solitons…

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…

Extending the gauge-invariance principle for \tau functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV,…

We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such solutions are forced to be exactly solitons…