Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

2019 ◽  
Vol 96 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Jian-Guo Liu ◽  
Qing Ye
Keyword(s):  
Fluid Mechanics ◽  
Variable Coefficients ◽  
Lump Solutions ◽  
Petviashvili Equation

Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid mechanics

2017 ◽  
Vol 31 (22) ◽  
pp. 1750122 ◽  
Author(s):  
Xiao-Yu Wu ◽  
Bo Tian ◽  
Han-Peng Chai ◽  
Yan Sun
Keyword(s):  
Fluid Mechanics ◽  
Symbolic Computation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Dispersive Waves ◽  
Lump Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Peak Location ◽  
Lump Wave

Under investigation in this letter is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters [Formula: see text], [Formula: see text] and [Formula: see text] which are all the real constants: When [Formula: see text] increases, amplitude of the lump wave increases, and location of the peak moves; when [Formula: see text] increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when [Formula: see text] changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.

Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

2019 ◽  
Vol 20 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jianqing Lü ◽  
Sudao Bilige ◽  
Xiaoqing Gao
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Special Case ◽  
Interaction Phenomenon

AbstractIn this paper, with the help of symbolic computation system Mathematica, six kinds of lump solutions and two classes of interaction solutions are discussed to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation via using generalized bilinear form with a dependent variable transformation. Particularly, one special case are plotted as illustrative examples, and some contour plots with different determinant values are presented. Simultaneously, we studied the trajectory of the interaction solution.

Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (15) ◽  
pp. 1850161 ◽  
Author(s):  
Yaqing Liu ◽  
Xiaoyong Wen
Keyword(s):  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Shallow Water Wave ◽  
Petviashvili Equation ◽  
Kink Soliton ◽  
Interaction Phenomena

In this paper, a generalized (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.

Lump solutions of a new generalized Kadomtsev–Petviashvili equation

2019 ◽  
Vol 33 (10) ◽  
pp. 1950126 ◽  
Author(s):  
Jing Yu ◽  
Wen-Xiu Ma ◽  
Shou-Ting Chen
Keyword(s):  
Differential Equation ◽  
Symbolic Computation ◽  
Transformation Formula ◽  
Lump Solutions ◽  
Petviashvili Equation ◽  
Free Parameters

A new generalized Kadomtsev–Petviashvili (GKP) equation is derived from a bilinear differential equation by taking the transformation [Formula: see text]. By symbolic computation with Maple, lump solutions, rationally localized in all directions in the space, to the GKP equation are presented. The obtained lump solutions contain a set of six free parameters, four of which should satisfy a nonzero determinant condition. As special examples, six particular lump solutions are constructed and depicted with [Formula: see text].

On a generalized Kadomtsev–Petviashvili equation with variable coefficients via symbolic computation

2007 ◽  
Vol 76 (5) ◽  
pp. 411-417 ◽  
Author(s):  
Li-Li Li ◽  
Bo Tian ◽  
Chun-Yi Zhang ◽  
Tao Xu
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficients ◽  
Petviashvili Equation

scholarly journals Wave packet pseudomodes of variable coefficient differential operators

2005 ◽  
Vol 461 (2062) ◽  
pp. 3099-3122 ◽  
Author(s):  
Lloyd N Trefethen
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Fluid Mechanics ◽  
Variable Coefficient ◽  
Differential Operators ◽  
High Accuracy ◽  
Variable Coefficients ◽  
Winding Number ◽  
Ordinary Differential Operators ◽  
Twist Condition

The pseudospectra of non-selfadjoint linear ordinary differential operators with variable coefficients are considered. It is shown that when a certain winding number or twist condition is satisfied, closely related to Hörmander's commutator condition for partial differential equations, ϵ -pseudoeigenfunctions of such operators for exponentially small values of ϵ exist in the form of localized wave packets. In contrast to related results of Davies and of Dencker, Sjöstrand & Zworski, the symbol need not be smooth. Applications in fluid mechanics, non-hermitian quantum mechanics and other areas are presented with the aid of high-accuracy numerical computations.

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