Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Nonlinear Dynamics - Fluid mechanics has the applications in a wide range of disciplines, such as oceanography, astrophysics, meteorology, and biomedical engineering. Under investigation in this...     

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...     

Characteristics of the solitary waves and lump waves with interaction phenomena in a (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation

In this paper, we consider a (\(2+1\))-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada (gCDGKS) equation, which is a higher-order generalization of the celebrated Kadomtsev–Petviashvili (KP) equation. By considering the Hirota bilinear form of the CDGKS equation, we study a type of exact interaction waves by the way of vector notations. The interaction solutions, which possess extensive applications in the nonlinear system, are composed by lump wave parts and soliton wave parts, respectively. Under certain conditions, this kind of solutions can be transformed into the pure lump waves or the stripe solitons. Moreover, we provide the graphical analysis of such solutions in order to better understand their dynamical behavior.     

New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada–Kotera model

In this paper, the (2+1)-dimensional Sawada–Kotera model is studied with the Hirota bilinear method, gauge transformation and symbolic computation. Based on an alternative bilinear representation of the model, a bilinear Bäcklund transformation (BT) with three arbitrary constants is derived. Via applying a gauge transformation to this BT and choosing suitable constant parameters, three other sets of bilinear BTs are constructed, among which, the last set is treated as a new bilinear BT and denoted as BTIV hereby. Finally, by performing the perturbation technique on the new bilinear BT, namely BTIV, multisoliton solutions are iteratively achieved, and as an example, the one-, two- and three-soliton solutions are explicitly given. Note that formulas of the soliton solutions obtained hereby through solving the BTIV are different from the previous ones in other literature.     

High-order lumps,high-order breathers and hybrid solutions for an extended (3 + 1)-dimensional Jimbo–Miwa equation in fluid dynamics

Nonlinear Dynamics - Under investigation in this letter is an extended (3 + 1)-dimensional Jimbo–Miwa (eJM) equation, which can be used to describe many nonlinear phenomena in mathematical...     

Interaction behaviors for the ( $$\varvec{2+1}$$ 2 + 1 )-dimensional Sawada–Kotera equation

Nonlinear Dynamics - The chimera state, exhibiting a hybrid state of coexisting coherent and incoherent behaviors, has become a fast growing field in the past decade. In this paper, we investigate...     

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.

     

The higher-order lump,breather and hybrid solutions for the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation in fluid mechanics

Nonlinear Dynamics - Under investigation in this paper is the (2 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation, which can be utilized to describe...     

New mixed solutions generated by velocity resonance in the $$(2+1)$$ ( 2 + 1 ) -dimensional Sawada–Kotera equation

Nonlinear Dynamics - Based on the N-soliton solutions of the $$(2+1)$$ -dimensional Sawada–Kotera equation, the collisions among lump waves, line waves, and breather waves are studied in this...     

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 (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 analysis,auto-Bäcklund transformation and analytic solutions of a (2 $$+$$ + 1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Nonlinear Dynamics - Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2 $$+$$ 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...     

Hybrid localized wave solutions for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

Nonlinear Dynamics - Based on the long wave limit method and complex conjugate condition technique, we investigate hybrid localized wave solutions with different forms for the generalized...     

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...     

Semi-rational solutions for a $$(2+1)$$ ( 2 + 1 ) -dimensional Davey–Stewartson system on the surface water waves of finite depth

Nonlinear Dynamics - Under investigation in this work is a $$(2+1)$$ -dimensional Davey–Stewartson system, which describes the surface water wave packets of finite depth. With respect to the...     

General soliton solutions to a $$varvec{(2+1)}$$ ( 2 + 1 ) -dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

Nonlinear Dynamics - In this paper, we study the existence and bifurcation of subharmonic solutions of a four-dimensional slow–fast system with time-dependent perturbations for the...