N-soliton solution of a coupled integrable dispersionless equation

<正>A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given.     

Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation

Nonlinear Dynamics - A novel complex nonlinear wave equation was recently found by Mukherjee and Kundu (Phys. Lett. A 383:985–990, 2019) and shown that it possesses the first-order rogue...     

N-soliton solutions of an integrable equation studied by Qiao

In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures.     

Periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation

2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.     

Smooth soliton and kink solutions for a new integrable soliton equation

Nonlinear Dynamics - We establish a relationship between a new integrable soliton equation and Gardner’s equation by a transformation. Then, we use this transformation and solutions of...     

Rogue wave solutions for the coupled cubic–quintic nonlinear Schrödinger equations in nonlinear optics

A generalized Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equation is constructed by the Darboux matrix method. As applications, the Nth-order rogue wave solutions of the coupled cubic–quintic nonlinear Schrödinger equation have been obtained. In particular, the dynamics of the general first- and second-order rogue waves are discussed and illustrated through some figures.     

Multiple Periodic-Soliton Solutions for （3＋1）-Dimensional Jimbo-Miwa Equation

2N line-soliton solutions of the （3＋1）-dimensional Jimbo-Miwa equation can be presented by resorting to the Hirota bilinear method. In this paper, N periodic-soliton solutions of the （3＋1）-dimensional Jimbo-Miwa equation are obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.     

Multi-peakon solutions to a four-component Camassa-Holm type system

A four-component Camassa-Holm type system with cubic nonlinearity is investigated. It allows an arbitrary function $\Gamma(x,t)$ to be involved in to include some existing integrable peakon equations as special reductions. We obtain $N$-peakon solutions of the four-component Camassa-Holm type system with two special cases of $\Gamma(x,t)$. In particular, we give one- and two-peakon solutions in an explicit formula and are graphically plotted. Further, some interesting peaked solutions are found: some peakon waves possessing positive and negative amplitudes while others decaying and growing amplitudes.     

New Multi-soliton Solutions for the （2＋1）-Dimensional Kadomtsev-Petviashvili Equation

In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.     

Multiple Periodic-Soliton Solutions for (3+1)-Dimensional Jimbo-Miwa Equation

2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting to the Hirota bilinear method. In this paper, N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation are obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.