scholarly journals Soliton solutions to a (2+1)-dimensional nonlocal NLS equation

2021 ◽  
Author(s):  
Qiaofeng Huang ◽  
Chenzhi Ruan ◽  
Jiaxing Huang
Keyword(s):  
Boundary Condition ◽  
Soliton Solutions ◽  
Kp Hierarchy ◽  
Nls Equation ◽  
Bilinear Method ◽  
Kp Hierarchy Reduction Method ◽  
Back Ground ◽  
Nonzero Boundary ◽  
Non Local ◽  
N Gram

Abstract In this paper, applying the Hirota’s bilinear method and the KP hierarchy reduction method, we obtain the general soliton solutions in the forms of N × N Gram-type determinants to a (2+1)-dimensional non-local nonlinear Schrodinger equation with time reversal under zero and nonzero boundary conditions. The general bright soliton solutions with zero boundary condition are derived via the tau functions of two-component KP hierarchy. Under nonzero boundary condition, we first construct general soliton solutions on periodic back-ground, when N is odd. Furthermore, we discuss typical dynamics of solutions analytically, and graphically.

Soliton solutions to the nonlocal Davey–Stewartson III equation

2020 ◽  
pp. 2150026
Author(s):  
Heming Fu ◽  
Chenzhen Ruan ◽  
Weiying Hu
Keyword(s):  
Positive Integer ◽  
Reduction Method ◽  
Soliton Solutions ◽  
Regularity Of Solutions ◽  
Kp Hierarchy ◽  
Bilinear Method ◽  
Suitable Parameter ◽  
Kp Hierarchy Reduction Method ◽  
Kp Hierarchy Reduction

The soliton solutions on both constant and periodic backgrounds of the nonlocal Davey–Stewartson III equation are derived by using the bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented as [Formula: see text] Gram-type determinants, with [Formula: see text] a positive integer. Typical dynamics of these soliton solutions are investigated in analytical and graphical aspects. Two types of soliton solutions are generated with different [Formula: see text]. When [Formula: see text] is even, solitons on the constant background can be constructed, whereas solitons appear on the periodic background for odd [Formula: see text]. Under suitable parameter restrictions, we show the regularity of solutions and display all patterns of two- and four-soliton solutions.

On a Riemann–Hilbert problem for the NLS-MB equations

2021 ◽  
pp. 2150420
Author(s):  
Leilei Liu ◽  
Weiguo Zhang ◽  
Jian Xu
Keyword(s):  
Hilbert Problem ◽  
Soliton Solutions ◽  
Coupled System ◽  
Soliton Interaction ◽  
Nls Equation ◽  
Nonzero Boundary ◽  
Complex Symmetric ◽  
Complex Phenomena ◽  
Symmetric Relations ◽  
Riemann Hilbert Problem

In this paper, we study a coupled system of the nonlinear Schrödinger (NLS) equation and the Maxwell–Bloch (MB) equation with nonzero boundary conditions by Riemann–Hilbert (RH) method. We obtain the formulae of the simple-pole and the multi-pole solutions via a matrix Riemann–Hilbert problem (RHP). The explicit form of the soliton solutions for the NLS-MB equations is obtained. The soliton interaction is also given. Furthermore, we show that the multi-pole solutions can be viewed as some proper limits of the soliton solutions with simple poles, and the multi-pole solutions constitute a novel analytical viewpoint in nonlinear complex phenomena. The advantage of this way is that it avoids solving the complex symmetric relations and repeatedly solving residue conditions.

N-soliton and rogue wave solutions of (2+1)-dimensional integrable system with Lax pair

2019 ◽  
Vol 33 (27) ◽  
pp. 1950317 ◽  
Author(s):  
Asma Issasfa ◽  
Ji Lin
Keyword(s):  
Integrable System ◽  
Differential Operators ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Rogue Waves ◽  
Bilinear Method ◽  
Kp Hierarchy Reduction Method ◽  
The Matrix ◽  
Linear Differential ◽  
Definition Of

A new generalized (2[Formula: see text]+[Formula: see text]1)-dimensional model, obtained from the Kadomtsev–Petviashvili (KP) equation considered as a system of nonlinear evolution partial differential equations (PDEs), is introduced. With the usage of the Hirota bilinear method and the KP-hierarchy reduction method, N-soliton solutions of the integrable system are constructed. Considering the case of s[Formula: see text]=[Formula: see text]−1 in the linear differential operators, L1 and L2, and a specific set of parameters, two dark solitons, mixed solutions consisting of soliton-type and periodic waves solution are obtained. Based on the particular definition of the matrix elements, one and two rogue waves solutions expressed in terms of rational functions are derived. It is shown that the fundamental rogue waves are line rogue waves, which is different from the property of the moving line solitons of the soliton equations.

scholarly journals Bright-Dark Mixed N-Soliton Solution of Two-Dimensional Multicomponent Maccari System

2017 ◽  
Vol 72 (8) ◽  
pp. 745-755 ◽  
Author(s):  
Zhong Han ◽  
Yong Chen
Keyword(s):  
Soliton Solution ◽  
Reduction Method ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Dark Solitons ◽  
Long Wave ◽  
Special Cases ◽  
Kp Hierarchy Reduction Method ◽  
Kp Hierarchy Reduction

AbstractBased on the KP hierarchy reduction method, we construct the general bright-dark mixed N-soliton solution of the two-dimensional (2D) (M+1)-component Maccari system comprised of M-component short waves (SWs) and one-component long wave (LW) with all possible combinations of nonlinearities. We firstly consider two types of mixed N-soliton solutions (two-bright-one-dark and one-bright-two-dark solitons in SW components) to the (3+1)-component Maccari system in detail. Then by extending our analysis to the (M+1)-component Maccari system, its general m-bright-(M–m)-dark mixed N-soliton solution is obtained. The formula obtained also contains the general all-bright and all-dark N-soliton solutions as special cases. For the two-bright-one-dark mixed soliton solution of the (3+1)-component Maccari system, it can be shown that solioff excitation and solioff interaction take place in the two SW components supporting bright solitons, whereas the SW component supporting dark solitons and the LW component possess V-type solitary and interaction.

Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

2017 ◽  
Vol 31 (32) ◽  
pp. 1750298 ◽  
Author(s):  
Meidan Chen ◽  
Biao Li
Keyword(s):  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

2020 ◽  
Vol 75 (12) ◽  
pp. 999-1007
Author(s):  
Rustam Ali ◽  
Anjali Sharma ◽  
Prasanta Chatterjee
Keyword(s):  
Wave Field ◽  
Soliton Solutions ◽  
Negative Ions ◽  
First Integral ◽  
Statistical Properties ◽  
Charged Dust ◽  
Bilinear Method ◽  
Electronegative Plasma ◽  
Kdv Equations ◽  
First Four Moments

AbstractHead-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

Multiple Soliton Solutions for a Variety of Coupled Modified Korteweg–de Vries Equations

2011 ◽  
Vol 66 (10-11) ◽  
pp. 625-631
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
De Vries ◽  
Coupled Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

We make use of Hirota’s bilinear method with computer symbolic computation to study a variety of coupled modified Korteweg-de Vries (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are obtained for each coupled equation. The resonance phenomenon of each coupled mKdV equation is proved not to exist.

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