相关论文: Construction of Nth-order rogue wave solutions for…

The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of…

The aim of this paper is to apply Hirota's bilinear method to the integrable discrete Manakov system in the focusing dispersion regime in order to construct and analyze soliton and breather solutions. After deriving the general bilinear…

In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…

We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…

Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is…

Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…

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 present a Lagrangian for the bilinear discrete KP (or Hirota-Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus…

We propose a new method based on the invariant properties of the ansatz of the Hirota method which have been discovered recently. This method allows one to construct new solutions for a certain class the dissipative equations classified by…

In this letter we examine the two-component Hirota (TH) equations which describes the pulse propagation in a coupled fiber with higher-order dispersion and self-steepening. As the TH equations is a complete integrable system, which admits a…

We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…

In this paper we first define hypermonogenic solutions of the Dirac operator in Rp x Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function…

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system…

Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a…

A nonlinear Schr\"odinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can…

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this…

This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…

Breather solutions are considered to be generally accepted models of rogue waves. However, breathers are not localized, while wavefields in nature can generally be considered as localized due to the limited spatial dimensions. Hence, the…

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the…

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and…