Found 423 Documents (Results 1–100)
For the shallow water waves: bilinear-form and similarity-reduction studies on a Boussinesq-Burgers system. (English) Zbl 07898343
Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili equation. (English) Zbl 07881979
Families of exact solutions of a generalized \((2+1)\)-dimensional Boussinesq type equation. (English) Zbl 07881956
Solitons and traveling waves structure for the Schrödinger-Hirota model in fluids. (English) Zbl 07874094
Abundant interaction solutions of the integrable \((1 + 1)\)-dimensional coupled KdV system. (English) Zbl 07871697
Bright solitons and interaction in the higher-order Gross-Pitaevskii equation investigated with Hirota’s bilinear method. (English) Zbl 07866165
Bilinear Bäcklund transformation, fission/fusion and periodic waves of a \((3+1)\)-dimensional Kadomtsev-Petviashvili equation for the shallow water waves. (English) Zbl 07858417
Breather transitions and their mechanisms of a (2+1)-dimensional sine-Gordon equation and a modified Boussinesq equation in nonlinear dynamics. (English) Zbl 07845333
New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation. (English) Zbl 1537.35306
A generalized sine-Gordon equation: reductions and integrable discretizations. (English) Zbl 07839653
Dynamics of controllable matter-wave solitons and soliton molecules for a Rabi-coupled Gross-Pitaevskii equation with temporally and spatially modulated coefficients. (English) Zbl 1534.35351
Exploring two-dimensional internal waves: a new three-coupled Davey-Stewartson system and physics-informed neural networks with weight assignment methods. (English) Zbl 1535.76026
Reviewer: Denys Dutykh (Le Bourget-du-Lac)
Rational and semi-rational solutions to the nonlocal Davey-Stewartson III equation. (English) Zbl 1531.35297
Bright Soliton solutions to the nonlocal Manakov equations of reverse-space type. (English) Zbl 1529.35484
Rogue wave solutions for the \((3 + 1)\)-dimensional generalized Camassa-Holm-Kadomtsev-Petviashvili equation. (English) Zbl 1540.35348
Various solutions of the (2+1)-dimensional Hirota-Satsuma-Ito equation using the bilinear neural network method. (English) Zbl 1541.35406
Multi-soliton solutions to the generalized Boussinesq equation of tenth order. (English) Zbl 07809628
General soliton and (semi-)rational solutions of a \((2+1)\)-dimensional sinh-Gordon equation. (English) Zbl 1529.35434
Tau-function formulation for bright, dark soliton and breather solutions to the massive Thirring model. (English) Zbl 1533.37138
Lump solution and interaction solutions to the fourth-order extended \((2+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. (English) Zbl 1529.37041
A novel investigation of extended (3+1)-dimensional shallow water wave equation with constant coefficients utilizing bilinear form. (English) Zbl 07749610
MSC:
76B15
Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients. (English) Zbl 1529.35516
An extended Hirota bilinear method and new wave structures of (2+1)-dimensional Sawada-Kotera equation. (English) Zbl 1529.35443
Rogue wave solutions of \((3 + 1)\)-dimensional Kadomtsev-Petviashvili equation by a direct limit method. (English) Zbl 1519.35058
Dark beam excitations in the defocusing \((2+1)\)-dimensional Zakharov system. (English) Zbl 1527.83044
Breather and nondegenerate solitons in the two-component modified Korteweg-de Vries equation. (English) Zbl 1530.35263
Lump, breather and interaction solutions to the (3+1)-dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation. (English) Zbl 1530.35210
\(n\)-soliton, breather, lump solutions and diverse traveling wave solutions of the fractional \((2+1)\)-Dimensional Boussinesq equation. (English) Zbl 1521.35142
Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle. (English) Zbl 1516.35355
Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation. (English) Zbl 07677981
Modulational instability and discrete localized modes in two coupled atomic chains with next-nearest-neighbor interactions. (English) Zbl 1509.82029
The integrability of a \((2+1)\)-dimensional nonlinear wave equation: Painlevé property, multi-order breathers, multi-order lumps and hybrid solutions. (English) Zbl 1524.70054
Hybrid soliton and breather waves, solution molecules and breather molecules of a \((3+1)\)-dimensional Geng equation in shallow water waves. (English) Zbl 1525.76022
Reviewer: Denys Dutykh (Le Bourget-du-Lac)
Shallow ocean soliton and localized waves in extended \((2 + 1)\)-dimensional nonlinear evolution equations. (English) Zbl 1516.86002
Soliton solution and asymptotic analysis of the three-component Hirota-Satsuma coupled KdV equation. (English) Zbl 1508.35137
Soliton solutions and lump-type solutions to the \((2+1)\)-dimensional Kadomtsev-Petviashvili equation with variable coefficient. (English) Zbl 1538.37038
A numerical study of \(N\)-periodic wave solutions to four integrable equations. (English) Zbl 1501.35120
In oceanography, acoustics and hydrodynamics: investigations on an extended coupled (2+1)-dimensional Burgers system. (English) Zbl 07851823
MSC:
65Mxx
Periodic kinetic Alfvén waves and overtaking between multi-solitons in nonthermal electron-positron-ion plasma. (English) Zbl 07851763
The dynamic characteristics of pure-quartic solitons and soliton molecules. (English) Zbl 1525.37080
Dynamical analysis of diversity lump solutions to the \((2+1)\)-dimensional dissipative Ablowitz-Kaup-Newell-Segure equation. (English) Zbl 1516.35359
Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation. (English) Zbl 1514.35420
Dynamics of mixed lump-soliton for an extended \((2+1)\)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. (English) Zbl 1514.35383
Higher-order smooth positons and breather positons of sine-Gordon equation. (English) Zbl 1511.37086
Multiple-order rogue wave solutions to a \((2+1)\)-dimensional Boussinesq type equation. (English) Zbl 1511.35309
Interaction of ion-acoustic solitons for multi-dimensional Zakharov Kuznetsov equation in van Allen radiation belts. (English) Zbl 1504.35430
On lump, periodic and travelling wave structures to the generalized breaking soliton model. (English) Zbl 1503.35059
Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed KdV equation using Hirota-bilinear approach. (English) Zbl 1516.35377
N-solitons, lump solution and interaction phenomenon to the Boussinesq equation. (English) Zbl 1513.30144
New local and nonlocal soliton solutions of a nonlocal reverse space-time mKdV equation using improved Hirota bilinear method. (English) Zbl 1511.35078
A direct method for generating rogue wave solutions to the \((3+1)\)-dimensional Korteweg-de Vries Benjamin-Bona-Mahony equation. (English) Zbl 1510.35010
The Davey-Stewartson I equation: doubly localized two-dimensional rogue lumps on the background of homoclinic orbits or constant. (English) Zbl 1492.35283
Considering the shallow water of a wide channel or an open sea through a generalized \((2+1)\)-dimensional dispersive long-wave system. (English) Zbl 1508.76018
Dynamics and numerical simulation of optical pulses in the passively mode-locked Er-doped fiber laser. (English) Zbl 1504.35513
Lump interaction phenomena to the nonlinear ill-posed Boussinesq dynamical wave equation. (English) Zbl 1492.35094
Wronskian and Grammian conditions, and Pfaffianization of an extended \((3+1)\)-dimensional Jimbo-Miwa equation. (English) Zbl 1540.35357
Dispersive optical solitons along with integrability test and one soliton transformation for saturable cubic-quintic nonlinear media with nonlinear dispersion. (English) Zbl 1490.35098
Degenerate soliton and breather solutions of the modified Korteweg-de Vries-Sine Gordon equation. (English) Zbl 1487.35180
Characteristics of lump-kink and their fission-fusion interactions, rogue, and breather wave solutions for a (3+1)-dimensional generalized shallow water equation. (English) Zbl 1499.35026
Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system. (English) Zbl 1484.35132
\(N\)-soliton, \(M\)-breather and hybrid solutions of a time-dependent Kadomtsev-Petviashvili equation. (English) Zbl 1540.35356
Bäcklund transformation and multi-soliton solutions for the discrete Korteweg-de Vries equation. (English) Zbl 1487.35341
Reviewer: Patrícia Nunes da Silva (Rio de Janeiro)
Soliton interaction of a generalized nonlinear Schrödinger equation in an optical fiber. (English) Zbl 1479.78024
Breather, lump and N-soliton wave solutions of the (2+1)-dimensional coupled nonlinear partial differential equation with variable coefficients. (English) Zbl 1497.35413
Interaction of multiple superposition solutions for the \((4 + 1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. (Interaction of multiple superposition solutions for the \((4 + 1)\)-dimensional Boiti-LeonManna-Pempinelli equation.) (English) Zbl 1537.35144
Construction of abundant solutions for two kinds of \((3+1)\)-dimensional equations with time-dependent coefficients. (English) Zbl 1517.37075
The abundant mixed solutions of \((2+1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation. (English) Zbl 1516.37093
Dynamics of lump solutions, lump-kink solutions and periodic lump solutions in a \((3+1)\)-dimensional generalized Jimbo-Miwa equation. (English) Zbl 1518.76010
A variety of multiple-soliton solutions for the integrable \((4+1)\)-dimensional Fokas equation. (English) Zbl 1538.35122
Multihumped nondegenerate fundamental bright solitons in \(N\)-coupled nonlinear Schrödinger system. (English) Zbl 1519.35302
Fractional isospectral and non-isospectral AKNS hierarchies and their analytic methods for \(N\)-fractal solutions with Mittag-Leffler functions. (English) Zbl 1494.35172
Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics. (English) Zbl 1494.35141
Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations. (English) Zbl 1525.35206
Cross-kink wave, solitary, dark, and periodic wave solutions by bilinear and He’s variational direct methods for the KP-BBM equation. (English) Zbl 1492.76021
MSC:
76B15
Lumps and interaction solutions to the \((4+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics. (English) Zbl 1496.37074
Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada-Kotera equation. (English) Zbl 1484.35136
Periodic wave solutions and stability analysis for the (3+1)-D potential-YTSF equation arising in fluid mechanics. (English) Zbl 1509.35235
Lump and interaction solutions for a generalized \((3 + 1)\)-dimensional propagation model of nonlinear waves in fluid dynamics. (English) Zbl 1479.35720
The soliton solutions and long-time asymptotic analysis for an integrable variable coefficient nonlocal nonlinear Schrödinger equation. (English) Zbl 1483.35200
Rogue waves, breather waves and soliton solutions for a deformed Boussinesq-type equation. (Chinese. English summary) Zbl 1488.35465
Soliton solutions to the reverse-time nonlocal Davey-Stewartson III equation. (English) Zbl 1524.35600
Analytical solutions for the coupled Hirota equations in the firebringent fiber. (English) Zbl 1510.35315
Hetero-Bäcklund transformation, bilinear forms and \(N\) solitons for a generalized three-coupled Korteweg-de Vries system. (English) Zbl 1477.35218
Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves. (English) Zbl 1476.35082
The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations. (English) Zbl 1525.35207
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