Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation

Zhang, Yanni; Pang, Jing

doi:10.1155/2019/7172860

Cited by 11 publications

(4 citation statements)

References 15 publications

(14 reference statements)

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“…( 5 ) in bilinear form, Now the function g and h in Eq. ( 8 ) can be assumed as Zhang and Pang ( 2019 ), we set g and h in the bilinear form (7) as, where . However, are all real parameters to be measured.…”

Section: Lump Solutionmentioning

confidence: 99%

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

et al. 2022

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This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation may be converted into plane systems. We use Hirota bilinear method to obtained these solutions. At the end, we present graphical representation of our results in various dimensions.

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Section: Lump Solutionmentioning

confidence: 99%

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

et al. 2022

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“…We will use the simplified Hirota's method to identify different soliton solutions to an eCBS equation. The extended Calogero-Bogoyavlenskii-Schiff equation is given in equation (2). Consider an algorithmic derivative transform…”

Section: Computing Solutions To An Ecbs Equationmentioning

confidence: 99%

“…Recently, the study of rational solutions of nonlinear partial differential equations (NPDEs) has attracted the interest of mathematicians, physicists, and many other scientists. These rational solutions [1][2][3][4][5], such as lump solutions and rogue wave solutions have been found in many integrable systems [6][7][8]. Manakov et al discovered the lump wave in [9].…”

Section: Introductionmentioning

confidence: 99%

Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

2021

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In this paper, we consider an extended Calogero-Bogoyavlenskii-Schiff (eCBS) equation. Based on a logarithmic derivative transform and with the aid of symbolic computation, we construct complex multiple solitons for this nonlinear model. Also, by using a symbolic computational method, one-lump solution, two-soliton solution, localized and breather wave solution, as well as a periodic wave solution and multiple wave solutions are obtained. The constraint conditions which ensure the validity of the wave structures are also reported. Besides, the graphs of the solution attained are recorded in 3D graphs by fixing parameters to discuss their dynamical properties. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.

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“…The (3 + 1)-dimensional VC B-type KP equation is extended from the KP equation and can explain some notable (3 + 1)-dimensional waves in fluid dynamics [37]. Also, Zhang and Pang [38] found the lump and lump-type solutions through the Hirota bilinear form for the variable-coefficient B-type Kadomtsev-Petviashvili equation.…”

Section: Introductionmentioning

confidence: 98%

Investigating One-, Two-, and Triple-Wave Solutions via Multiple Exp-Function Method Arising in Engineering Sciences

Wan

Manafian

Ismael

et al. 2020

Advances in Mathematical Physics

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The multiple Exp-function method is employed for searching the multiple soliton solutions for the new extended (3+1)-dimensional Jimbo-Miwa-like (JM) equation, the extended (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) equation, the generalization of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (BK) equation, and a variable-coefficient extension of the DJKM (vDJKM) equation, which contain one-soliton-, two-soliton-, and triple-soliton-kind solutions. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values.

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Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation

Cited by 11 publications

References 15 publications

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

Investigating One-, Two-, and Triple-Wave Solutions via Multiple Exp-Function Method Arising in Engineering Sciences

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