Study on the (3+1)-dimensional KP equation with lump solution and its collision phenomena

2021 ◽  
Author(s):  
Ling-Ling Zhang ◽  
Xin Wang
Keyword(s):  
Bilinear Form ◽  
Periodic Wave ◽  
The Other ◽  
Periodic Wave Solution ◽  
Lump Solution ◽  
Kp Equation ◽  
Hirota Bilinear Form ◽  
Picture Description ◽  
Hirota Bilinear ◽  
Kink Soliton

The (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied in this paper by constructing the Hirota bilinear form. The lump solution of the equation is obtained by bilinear form, and the conditions for the existence of the solution are obtained. The picture description of lump solution is further given. On the other hand, we also give the collision phenomena of lump solution, periodic wave solution and a single-kink soliton solution when the (3+1)-dimensional KP equation reduces to [Formula: see text] and [Formula: see text] by means of the Hirota method. The collision phenomenon is shown in the 3D plot description, the dynamic characteristics of the collision are also analyzed.

scholarly journals Theta Function Solutions of the 3 + 1-Dimensional Jimbo-Miwa Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ting Su ◽  
Hui-Hui Dai
Keyword(s):  
Theta Function ◽  
Bilinear Form ◽  
Wave Solution ◽  
Asymptotic Properties ◽  
Periodic Wave ◽  
Periodic Wave Solution ◽  
Periodic Waves ◽  
Variable Transformation ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear

The 3 + 1-dimensional Jimbo-Miwa equation can be written into a Hirota bilinear form by the dependent variable transformation. We give its one-periodic wave solution and two-periodic wave solution by utilizing multidimensional elliptic Θ-function. With the help of the solution curves, the asymptotic properties of the periodic waves are analyzed in detail.

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

Characteristics of the breather waves, lump waves and semi-rational solutions in a generalized (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

2019 ◽  
Vol 33 (28) ◽  
pp. 1950350 ◽  
Author(s):  
Wei-Qi Peng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang
Keyword(s):  
Bilinear Form ◽  
Rational Solutions ◽  
Bell Polynomial ◽  
Long Wave ◽  
Hirota Bilinear Form ◽  
Wave Limit ◽  
Parameter Constraints ◽  
Hirota Bilinear

In this work, we study a generalized (2[Formula: see text]+[Formula: see text]1)-dimensional asymmetrical Nizhnik–Novikov–Veselov (NNV) equation. Its Hirota bilinear form is constructed via the Bell polynomial. Based on the obtained bilinear form, the Nth-order breather waves are derived explicitly under certain parameter constraints. Moreover, we generate the nonsingular Nth-order lump waves through applying the long wave limit method. Additionally, we successfully present the semi-rational waves containing the combination of lump waves and single-soliton waves, the combination of lump waves and breather waves.

Lump solutions to the BKP equation by symbolic computation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640028 ◽  
Author(s):  
Jing-Yun Yang ◽  
Wen-Xiu Ma
Keyword(s):  
Symbolic Computation ◽  
Kp Equation ◽  
Lump Solutions ◽  
Positivity Condition ◽  
Independent Variables ◽  
Computation Process ◽  
Starting Point ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear ◽  
Bkp Equation

Lump solutions are rationally localized in all directions in the space. A general class of lump solutions to the (2+1)-dimensional B-Kadomtsev–Petviashvili (BKP) equation is presented through symbolic computation with Maple. The Hirota bilinear form of the equation is the starting point in the computation process. Like the KP equation, the resulting lump solutions contain six arbitrary parameters. Two of the parameters are due to the translation invariances of the BKP equation with the independent variables, and the other four need to satisfy a nonzero determinant condition and the positivity condition, which guarantee analyticity and rational localization of the solutions.

Lump-type solutions for the (4+1)-dimensional Fokas equation via symbolic computations

2017 ◽  
Vol 31 (25) ◽  
pp. 1750224 ◽  
Author(s):  
Li Cheng ◽  
Yi Zhang
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Symbolic Computations ◽  
Hirota Bilinear Form ◽  
Free Parameters ◽  
Almost All ◽  
Hirota Bilinear

Based on the Hirota bilinear form, two classes of lump-type solutions of the (4[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Fokas equation, rationally localized in almost all directions in the space are obtained through a direct symbolic computation with Maple. The resulting lump-type solutions contain free parameters. To guarantee the analyticity and rational localization of the solutions, the involved parameters need to satisfy certain constraints. A few particular lump-type solutions with special choices of the involved parameters are given.

Interaction solutions for the (2+1)-dimensional Ito equation

2019 ◽  
Vol 33 (13) ◽  
pp. 1950167 ◽  
Author(s):  
Yaning Tang ◽  
Jinli Ma ◽  
Wenxian Xie ◽  
Lijun Zhang
Keyword(s):  
Periodic Function ◽  
Rational Function ◽  
Bilinear Form ◽  
Hyperbolic Function ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Hirota Bilinear Form ◽  
Dynamical Properties ◽  
Hirota Bilinear ◽  
Ito Equation

In this paper, two classes of interaction solutions of the (2[Formula: see text]+[Formula: see text]1)-dimensional Ito equation are studied in the case of Hirota bilinear form. As the results, the interaction solutions between the rational function and a periodic function as well as the interaction solution between the hyperbolic function and a periodic function are obtained. Based on the interaction solutions, a new transformation is proposed to analyze and discuss the influence of parameters. Furthermore, two kinds of lump solutions can be obtained via the limit behavior of the interaction solutions and the dynamical properties of these solutions are also illustrated.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Yanni Zhang ◽  
Jing Pang
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Variable Coefficient ◽  
Three Dimensional ◽  
Petviashvili Equation ◽  
Hirota Bilinear Form ◽  
Contour Plots ◽  
Dimensional Variable ◽  
Hirota Bilinear

Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by taking special choices of the involved parameters. The property of solutions is investigated and exhibited vividly by three-dimensional plots and contour plots.

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