Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation

The new (2+1)-dimensional generalized KdV equation which exists the bilinear form is mainly discussed. We prove that the equation does not admit the Painlevé property even by taking the arbitrary constant a=0. However, this result is different from Radha and Lakshmanan??s work. In addition, based on Hirota bilinear method, periodic wave solutions in terms of Riemann theta function and rational solutions are derived, respectively. The asymptotic properties of the periodic wave solutions are analyzed in detail.     

A (2+1)-dimensional combined KdV–mKdV equation: integrability,stability analysis and soliton solutions

Nonlinear Dynamics - In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check...     

Painlevé integrability and N-soliton solution for the variable-coefficient Zakharov–Kuznetsov equation from plasmas

With the help of symbolic computation, this paper investigates the variable-coefficient Zakharov–Kuznetsov equation which governs the two-dimensional ion-acoustic waves obliquely propagating in an inhomogeneous magnetized two-ion-temperature dusty plasma. The integrability of this model is examined through the Painlevé analysis. Via the Hirota method, the bilinear form of such model is derived. Based on the obtained bilinear form, the N-soliton solution is constructed. Propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis.     

Bell-polynomial approach and soliton solutions for the Zhiber–Shabat equation and (2+1)-dimensional Gardner equation with symbolic computation

Under investigation in this paper are the Zhiber?CShabat and (2+1)-dimensional Gardner equations in quantum fields, fluids and plasmas. Via the Hirota method and symbolic computation, the Bell-polynomial approach is performed to directly bilinearize those equations. For the Zhiber?CShabat equation, based on the bilinear form with an auxiliary variable, the bell-shaped soliton, upside-down bell-shaped soliton and breather-like solutions are obtained. Figures are plotted to illustrate the elastic interactions between two upside-down bell-shaped solitons and the interaction between the breather-like. As to the (2+1)-dimensional Gardner equation, bilinear form, B?cklund transformation, one- and two-shock wave solutions are derived. Amplitude-compression and amplification interactions are investigated analytically and graphically.     

A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions

Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend the classic lower-dimensional integrable models to arbitrary spatial dimension. We investigate the celebrated Kadomtsev–Petviashvili (KP) equation and propose its (n+1)-dimensional integrable extension. Based on the singularity manifold analysis and binary Bell polynomial method, it is found that the (n+1)-dimensional generalized KP equation has N-soliton solutions, and it also possesses the Painlevé property, Lax pair, Bäcklund transformation as well as infinite conservation laws, and thus the (n+1)-dimensional generalized KP equation is proven to be completely integrable. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.

     

Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system

Nonlinear Dynamics - In this article, Painlevé analysis is employed to test the integrability of (2+1)-dimensional long wave–short wave resonance interaction system using the...     

Bilinear form,soliton, breather,lump and hybrid solutions for a ( $$varvec{2+1}$$ 2 + 1 )-dimensional Sawada–Kotera equation

Nonlinear Dynamics - In this paper, we investigate a ( $$2+1$$ )-dimensional Sawada–Kotera (SK) equation for the atmosphere, rivers, lakes, oceans, as well as the conformal field and...     

Abundant lump and lump–kink solutions for the new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

Nonlinear Dynamics - By utilizing the Hirota’s bilinear form and symbolic computation, abundant lump solutions and lump–kink solutions of the new (3 + 1)-dimensional...     

Interaction solutions between lump and stripe soliton to the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Nonlinear Dynamics - In this paper, we apply the ansatz method to the multi-linear form of the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation for constructing interaction...     

Painlevé analysis,Lie symmetries,and exact solutions for the time-dependent coefficients Gardner equations

In this paper, the three variable-coefficient Gardner (vc-Gardner) equations are considered. By using the Painlevé analysis and Lie group analysis method, the Painlevé properties and symmetries for the equations are obtained. Then the exact solutions generated from the symmetries and Painlevé analysis are presented.     

Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term

Nonlinear Dynamics - The (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical...     

Auto-Bäcklund transformations and soliton solutions on the nonzero background for a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid

In this paper, a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid is investigated. By the virtue of the truncated Painlevé expansion, a set of the auto-Bäcklund transformations of that equation is worked out. Based on the auto-Bäcklund transformations with certain non-trivial seed solutions, one-, two-, three- and N-soliton solutions on the nonzero background of that equation are derived with N as a positive integer. According to those two-soliton solutions, X- and inelastic-type soliton solutions are obtained. Via the asymptotic analysis, influence of the coefficients for the above equation is discussed and the interactions between the solitons are also studied. Then, those solitons and interactions are shown graphically.

     

New interaction of high-order breather solutions,lump solutions and mixed solutions for (3+1)-dimensional Hirota–Satsuma–Ito-like equation

Nonlinear Dynamics - Under investigation in this letter is an (3+1)-dimensional Hirota–Satsuma–Ito-like equation, which provide strong support for studying the dynamic behavior of...