DOI10.1088/0305-4470/36/9/307zbMath1039.37061OpenAlexW1977886141MaRDI QIDQ4466199
Xiangguo Geng
Publication date: 9 June 2004
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0305-4470/36/9/307
A (2 + 1)-dimensional breaking soliton equation associated with the Kaup-Newell soliton hierarchy ⋮
Exact traveling wave solutions to the \((2 + 1)\)-dimensional Jaulent-Miodek equation ⋮
Bäcklund transformation and solutions of a \((3+1)\)-dimensional nonlinear evolution equation ⋮
On the solutions and conservation laws of a coupled Kadomtsev-Petviashvili equation ⋮
Four \((2 + 1)\)-dimensional integrable extensions of the Kadomtsev-Petviashvili equation ⋮
DECOMPOSITION AND STRAIGHTENING OUT OF THE DISCRETE KAUP–NEWELL FLOWS ⋮
Painlevé analysis, \({\Phi}\)-integrable and exact solutions to the \((3+1)\)-dimensional nonlinear evolution equations ⋮
Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation ⋮
Resonant multiple wave solutions for a \((3+1)\)-dimensional nonlinear evolution equation by linear superposition principle ⋮
\(N\)-soliton solutions and long-time asymptotic analysis for a generalized complex Hirota-Satsuma coupled KdV equation ⋮
New explicit traveling wave solutions for three nonlinear evolution equations ⋮
Breathers, interactions between breathers and lumps for a (3 + 1)-dimensional nonlinear evolution equation for the shallow-water waves ⋮
Soliton solutions for some nonlinear partial differential equations in mathematical physics using He's variational method ⋮
Multi-soliton and Pfaffian solutions of a \((2+1)\)-dimensional nonlinear evolution equation via the Jaulent-Miodek hierarchy ⋮
Reduction in the \((4+1)\)-dimensional Fokas equation and their solutions ⋮
Rogue waves and rational solutions of a \((3+1)\)-dimensional nonlinear evolution equation ⋮
An optimal system of Lie subalgebras and group-invariant solutions with conserved currents of a \((3+1)\)-D fifth-order nonlinear model I with applications in electrical electronics, chemical engineering and pharmacy ⋮
Riemann theta function solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera hierarchy ⋮
Lump and new interaction solutions to the (3+1)-dimensional nonlinear evolution equation ⋮
Invariance analysis, optimal system, and group invariant solutions of (3+1)‐dimensional non‐linear MA‐FAN equation ⋮
Hybrid soliton and breather waves, solution molecules and breather molecules of a \((3+1)\)-dimensional Geng equation in shallow water waves ⋮
A new approach to investigate the nonlinear dynamics in a \((3 + 1)\)-dimensional nonlinear evolution equation via Wronskian condition with a free function ⋮
Antidark solitons and soliton molecules in a \((3 + 1)\)-dimensional nonlinear evolution equation ⋮
Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation ⋮
Rational solutions for a (3+1)-dimensional nonlinear evolution equation ⋮
Algebro-geometric solutions of the sine-Gordon hierarchy ⋮
Two new Wronskian conditions for the (3+1)-dimensional Jimbo-Miwa equation ⋮
Multiple kink solutions and multiple singular kink solutions for (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy ⋮
New types of doubly periodic standing wave solutions for the coupled Higgs field equation ⋮
Some \((2 + 1)\)-dimensional nonlocal ``breaking soliton-type systems ⋮ New lump, lump-kink, breather waves and other interaction solutions to the (3+1)-dimensional soliton equation ⋮ \(N\)-soliton solutions and dynamic property analysis of a generalized three-component Hirota-Satsuma coupled KdV equation ⋮ The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations ⋮ Two hierarchies of new nonlinear evolution equations associated with \(3 \times 3\) matrix spectral problems ⋮ Extended Gram-type determinant, wave and rational solutions to two (3+1)-dimensional nonlinear evolution equations ⋮ The modified semi-discrete two-dimensional Toda lattice with self-consistent sources ⋮ Two different classes of Wronskian conditions to a \((3 + 1)\)-dimensional generalized shallow water equation ⋮ M-lump solutions to a \((3+1)\)-dimensional nonlinear evolution equation ⋮ The generalized dressing method with applications to variable-coefficient coupled Kadomtsev-Petviashvili equations ⋮ Rogue waves of a \((3+1)\)-dimensional nonlinear evolution equation ⋮ New multi-soliton solutions of a \((3+1)\)-dimensional nonlinear evolution equation ⋮ Two \((2+1)\)-dimensional soliton equations and their quasi-periodic solutions ⋮ Rational solutions for a \((2+1)\)-dimensional nonlinear model in water waves generated by the Jaulent-Miodek hierarchy ⋮ Quasi-periodic solutions of mixed AKNS equations ⋮ Quasi-periodic wave solution and asymptotic behavior for the \((2+1)\)-dimensional Toda lattice equation ⋮ Multiple rogue wave, dark, bright, and solitary wave solutions to the KP-BBM equation ⋮ \(N\)-soliton solution and its Wronskian form of a \((3+1)\)-dimensional nonlinear evolution equation ⋮ Rogue waves, breather waves and solitary waves for a (3+1)-dimensional nonlinear evolution equation ⋮ A new fractional order soliton equation hierarchy and its integrable coupling system ⋮ New \((3+1)\)-dimensional nonlinear evolution equations with mKdV equation constituting its main part: multiple soliton solutions ⋮ Explicit quasi-periodic solutions of the Kaup-Newell hierarchy ⋮ Periodic-wave solutions of the two-dimensional Toda lattice equation by a direct method ⋮ New (3+1)-dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions ⋮ Diversity of exact solutions to a (3 + 1)-dimensional nonlinear evolution equation and its reduction ⋮ Fission and fusion collision of high-order lumps and solitons in a \((3+1)\)-dimensional nonlinear evolution equation ⋮ DARBOUX TRANSFORMATION AND VARIOUS SOLUTIONS FOR A NONLINEAR EVOLUTION EQUATION IN (3 + 1)-DIMENSIONS ⋮ Multiple soliton solutions for (2 + 1)-dimensional Sawada-Kotera and Caudrey-Dodd-Gibbon equations ⋮ High-Order Lump-Type Solutions and Their Interaction Solutions to a (3+1)-Dimensional Nonlinear Evolution Equation* ⋮ Quasi-Periodic Solutions of Coupled KDV Type Equations ⋮ POSITON, NEGATON, SOLITON AND COMPLEXITON SOLUTIONS TO A FOUR-DIMENSIONAL NONLINEAR EVOLUTION EQUATION ⋮ Bilinear form and solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow-water waves ⋮ Further study of the localized solutions of the (2+1)-dimensional B-Kadomtsev-Petviashvili equation ⋮ Four \((2+1)\)-dimensional integrable extensions of the KdV equation: multiple-soliton and multiple singular soliton solutions ⋮ A \((3+1)\)-dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutions ⋮ Dynamical soliton wave structures of one-dimensional Lie subalgebras via group-invariant solutions of a higher-dimensional soliton equation with various applications in ocean physics and mechatronics engineering ⋮ PDEPtest: a package for the Painlevé test of nonlinear partial differential equations ⋮ Soliton solutions and quasiperiodic solutions of modified Korteweg–de Vries type equations ⋮ A study on lump and interaction solutions to a \((3+1)\)-dimensional soliton equation ⋮ The quasi-periodic solutions of mixed KdV equations
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