Keywords: The multiple-term fractional Kolmogorov-Petrovskii-Piskunov equation; Lie symmetry analysis; Symmetry reduction; Conservation laws; Analytic solutions; 35Q51; 35Q53; 35C99; 68W30; 74J35;
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Keywords: 35Q35; 35Q51; Boussinesq-Burgers equations; Initial-boundary value problem; Dynamic boundary conditions; Global well-posedness; Long-time behavior;
Keywords: 35Q51; 37K40; 35Q53; Soliton; Integrable equation; Hirota bilinear form; Lump solution;
Keywords: 37K10; 35Q51; 15A15; Moment modification; Nonisospectral Camassa-Holm type equation; Peakon solutions;
Keywords: primary; 35Q51; 35Q53; secondary; 37K10; 37K40; Gardner equation; Modified KdV equation; Breather; Stability;
Keywords: Classical Heisenberg ferromagnet equation; Soliton solutions; Inverse scattering transform; Magnetic droplet; Ferromagnetic materials; 35C08; 35G25; 35P25; 35Q40; 35Q51;
Keywords: Coupled nonlinear Schrödinger system; Bright soliton; Gauge transformation; Lax pair; 37K40; 35Q51; 35Q55;
Keywords: 35Q51; 37K10; 37K15; 37K40; Harry Dym; Invertible point transformation; High-frequency limit; Multi-phase solutions; Lax pair;
Keywords: Periodic Toda lattice hierarchy; Hill's equation; An integral source; Inverse spectral problem; Trace formulas; Primary 39A23; 35Q51; Secondary 34K13; 34K29;
Keywords: Tanh–coth scheme; Nonlinear schrödinger zakharov system; Solitons solutions35C05; 35Q51; 35B10
Keywords: 35J61; 35Q51; 35Q55Schrödinger equations; Saturable media; Concentration phenomena; Singularly perturbed elliptic equation; Asymptotically linear nonlinearities; Penalization methods
Keywords: 35G20; 35Q35; 35Q51; 47J35; 53B20; Third order differential equations; Pseudospherical surfaces; Spherical surfaces; Nonlinear partial differential equations;
Keywords: 78A60; 37K10; 35Q51; 35Q5502.30.Jr; 05.45.Yv; 02.30.Ik060.2310; 060.4510; 060.5530; 190.3270; 190.4370Solitons; Integrability; Semi-inverse variational principle
Keywords: Variant Boussinesq equation with dissipation term; shape analysis; bounded traveling wave solution; error estimate; dissipation effect35G20; 35Q35; 35Q51
Keywords: 35C08; 35Q51; 65M06Modified sine-Gordon equation; Impurity; Kink; Resonance dynamics
Keywords: 41A60; 35Q51; 35Q15Riemann–Hilbert problem; Integrable system; Coupled nonlinear Schrödinger equation; Initial–boundary value problem; Dirichlet-to-Neumann map
Existence and uniqueness of ground states for p-Choquard model
Keywords: 35Q51; 35Q40; 35Q55; 49S05; p-Choquard equation; Nonlocal nonlinearity; Ground state;
Miura and auto-Bäcklund transformations for the discrete KP and mKP hierarchies and their constrained cases
Keywords: The dKP and mdKP hierarchies; The cdKP and cmdKP hierarchies; Miura transformation; Auto-Bäcklund transformation; 02.30.Ik; 35Q51; 37K10; 37K40;
Families of semi-rational solutions to the Kadomtsev-Petviashvili I equation
Keywords: Kadomtsev-Petviashvili I equation; KP hierarchy reduction method; Breathers; Lumps; Semi-rational solutions; 35Q51; 35Q55; 37K10; 37K35; 37K40;
Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs
Keywords: 35Q51; 35Q53; 37K40; Symbolic computation; Lump solution; Interaction solution;
Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrödinger equations
Keywords: Nonlocal discrete nonlinear Schrödinger equation; Bilinear; Reduction; Double Casoratian solutions; 35Q51; 35Q55;
Two (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations: Breather, rational and semi-rational solutions
Keywords: PT-symmetry; Bilinear method; Breather solution; Rational solution; Semi-rational solution; 35C08; 35Q51; 37K10; 37K35,;
New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing
Keywords: Coupled nonlinear Schrödinger system; Soliton; Breathers; Darboux transformation; Lax pair; Four-wave mixing; 37K40; 35Q51; 35Q55;
General high-order breathers and rogue waves in the (3+1)-dimensional KP-Boussinesq equation
Keywords: (3+1)-dimensional KP-Boussinesq equation; Rogue wave solution; Bilinear method; Breather solution; 35Q51; 35Q55; 37K10; 37K35; 37K40;
A new nonlinear wave equation: Darboux transformation and soliton solutions
Keywords: 35Q51; 37K10; 35Q58; 35L65; Nonlinear wave equation; Darboux transformation; Soliton solutions;
An integrable system with peakon, complex peakon, weak kink, and kink-peakon interactional solutions
Keywords: 37K10; 35Q51; 35Q58; Generalization of Camassa-Holm equation; Peakon; Complex peakon; Weak kink; Lax pair; Integrable system;
Soliton curves in three-dimensional space forms
Keywords: 35Q51; 37K25; 53A04; 74K10; Soliton curves; Localized induction equation; Localized induction hierarchy;
An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
Keywords: 37K10; 35Q51; 15A15; Multipeakons; Pfaffian; Novikov equation; Toda lattice of BKP type;
Orbital stability of solitary waves for generalized Boussinesq equation with two nonlinear terms
Keywords: Generalized Boussinesq equation; Nonlinear terms; Solitary wave; Orbital stability; 35Q35; 35Q51; 37K45;
Exact solutions of space-time fractional EW and modified EW equations
Keywords: Fractional EW equation; Fractional MEW equation; Bright soliton; Singular solution; 35R10; 35Q51; 35L05; 26A33;
On periodic wave solutions of the KdV6 equation via bilinear Bäcklund transformation
Keywords: 35B10; 35Q51; 37K40; KdV6 equation; Bilinear Bäcklund transformation; Periodic wave solutions; Dynamical behaviors;
A new integrable symplectic map by the binary nonlinearization to the super AKNS system
Keywords: 35Q51; 37J10; 37K10; 37K30; Orthosymplectic Lie superalgebras; Super AKNS hierarchy; Explicit symmetry constraint; Binary nonlinearization;
Collisional dynamics of solitons in the coupled PT symmetric nonlocal nonlinear Schrödinger equations
Keywords: PT symmetry; Coupled nonlinear Schrödinger system; Bright soliton; Dark soliton; Darboux transformation; Lax pair; 37K40; 35Q51; 35Q55;
Differential Galois theory and Darboux transformations for Integrable Systems
Keywords: primary; 12H05; secondary; 35Q51; 37K10; Differential Galois theory; Picard-Vessiot theory; Integrability; Darboux transformations; Solitons;
Orbital stability of periodic traveling-wave solutions for the log-KdV equation
Keywords: 76B25; 35Q51; 35Q53; Orbital stability; Log-KdV equation; Periodic waves;
Exact solutions for the perturbed nonlinear Schrödinger equation with power law nonlinearity and Hamiltonian perturbed terms
Keywords: 78A60; 37 K10; 35Q51; 35Q55; Sine-cosine method; Jacobi elliptic equation method; Generalized Kudryashov method; Riccati equation method; Nonlinear Schrödinger equation; Exact solutions; Hyperbolic and trigonometric function solutions; Bright, dark, si
Constructing of exact solutions to the nonlinear Schrödinger equation (NLSE) with power-law nonlinearity by the Weierstrass elliptic function method
Keywords: 35Q53; 35B; 35Q51; 37K10Travelling wave solutions; Weierstrass elliptic function method; Nonlinear Schrödinger Equation (NLSE)
Twisted Ricci flow on a class of Finsler metrics and its solitons
Keywords: 35A07; 35K15; 35Q51; 53B40Twisted Ricci flow; (α,β)(α,β)-metric; Soliton
On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation
Keywords: A (3+1)-dimensional generalized KdV-like model equation; Bell polynomial; Bäcklund transformation; Lax pairs; Soliton solution; Periodic wave solution; 35Q51; 35Q53; 35C99; 68W30; 74J35;
Standing waves for discrete Schrödinger equations in infinite lattices with saturable nonlinearities
Keywords: 35Q51; 35Q55; 39A12; 39A70Discrete nonlinear Schrödinger equations; Saturable nonlinearities; Nontrivial solitons; Spectral gap; Spectral endpoint
Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice
Keywords: primary; 37K15; 37K40; secondary; 35Q51; 34A55; Multipeakons; Camassa-Holm; Inverse spectral problem; Kac-van Moerbeke lattice;
Topological and non-topological soliton solutions of Hamiltonian amplitude equation by He’s semi-inverse method and ansatz approach
Keywords: 35Q51; 37K40; 35Q80He’s semi-inverse method; Ansatz method; Hamiltonian amplitude equation
A note on the quasi-periodic solutions of the modified Boussinesq hierarchy
Keywords: 35Q51; 37K10; 14H70; 35C99The modified Boussinesq hierarchy; Explicit quasi-periodic solutions; Trigonal curve
Existence of positive ground state solutions for Kirchhoff type problems
Keywords: 35Q55; 35Q51; 53C35Kirchhoff type problem; Ground state solution; Pohozăev identity; Variational method
Existence of periodic travelling wave solutions for a regularized Benjamin–Ono system
Keywords: 42A45; 47A75; 35Q51; 76M45Regularized BO equation; Internal waves; Periodic travelling wave solutions; Pseudospectral methods
Soliton perturbation theory of Biswas–Milovic equation
Keywords: 35Q51; 35Q53; 37K10; 78A6002.30.Ik; 02.30.Jr; 42.81.Dp; 52.35.SbBiswas–Milovic equation; Soliton perturbation theory; Optical solitons; Adiabatic variations
Quasi-periodic solutions to the two-component nonlinear Klein-Gordon equation
Keywords: 35Q51; 37K10; 14H70; 35C99; Two-component nonlinear Klein-Gordon equation; Quasi-periodic solutions; Trigonal curve;
Optical quasi-solitons by Lie symmetry analysis
Keywords: 78A60; 35Q51; 35Q55; 37K10Quasi-solitons; Integrability; Nonlinearity; Kerr law; Power law; Parabolic law; Saturable law; Logarithmic law
Effects of the amplifier location in interchannel soliton collisions in periodic dispersion maps in the presence of third order dispersion
Keywords: 35A15; 35Q51; 37K40; 42.65Sf; 42.65.Tg; 42.81Dp; Optical solitons; Dispersion management; Wavelength division multiplexing; Third order dispersion; Optical fiber communication;
Hidden solitons in the Zabusky-Kruskal experiment: Analysis using the periodic, inverse scattering transform
Keywords: 05.45.Yv; 02.30.Ik; 35Q51; 35P25; Hidden solitons; Korteweg-de Vries equation; Inverse scattering transform; Nonlinear Fourier analysis;