Keywords: Finite-dimensional system; Liouville integrability; Bi-Hamiltonian system; Involutive solutions; Soliton hierarchy; 37K05; 37K10; 35Q53;
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Keywords: The multiple-term fractional Kolmogorov-Petrovskii-Piskunov equation; Lie symmetry analysis; Symmetry reduction; Conservation laws; Analytic solutions; 35Q51; 35Q53; 35C99; 68W30; 74J35;
Keywords: primary; 35Q53; 37K10; 35C07; Camassa-Holm equation; Cauchy problem; Analytic data; Global in time solutions; Analytic spaces; Exponential lower bound on the radius of analyticity;
Keywords: 35Q51; 37K40; 35Q53; Soliton; Integrable equation; Hirota bilinear form; Lump solution;
Keywords: primary; 35Q53; secondary; 35B40; Zakharov-Kuznetsov equation; Initial-boundary value problem; Global solution; Decay; Controllability;
Keywords: primary; 35Q53; secondary; 35B40; Zakharov-Kuznetsov equation; Initial-boundary value problem; Global solution; Decay;
Keywords: primary; 35Q51; 35Q53; secondary; 37K10; 37K40; Gardner equation; Modified KdV equation; Breather; Stability;
Keywords: Generalized Fisher equation; Traveling wave fronts; Geometric singular perturbation theory; Asymptotic behavior; Uniqueness; 34E15; 34D15; 35Q53; 35C07;
Keywords: 35Q53; 35B06; 35B40; 35S30; 45K05; Nonlocal equation; Solitary solutions; Symmetry; Exponential decay;
Keywords: 35Q30; 35Q35; 35Q40; 35Q53; 35Q55; 76D05; 76Y07; Incompressible viscous and diffusive MHD system; Ideal MHD system; Anisotropic inviscid MHD system; Boundary layer for no-slip boundary conditions;
Keywords: 35Q53; 37K10; 35C07; Camassa-Holm equation; Novikov equation; Cauchy problem; Global in time solutions; Analytic spaces; Lower bound on the radius of analyticity;
Keywords: 35Q53; 35B35; 37C20; Hunter-Saxton equations; Generic regularity; Lipschitz metric; Conservative solution;
Keywords: 35B32; 35B35; 35Q53; Bifurcation; Zakharov-Kuznetsov equation; Line solitary wave; Transverse instability; Asymptotic stability;
Keywords: Adjoint equation to nonlinear equations; Conservation laws; Multipliers; Partial differential equations; Symmetries35C07; 35Q53
Keywords: Predictor–corrector; Ring wave; Returning effect; Slope modulation35Q51; 35Q53; 65M06; 74J30; 94A14
Keywords: Global well-posedness; 3D Klein-Gordon-Zakharov equation; dyadic Xs,b spaces in higher dimension35E15; 35Q53
Keywords: 14H70; 17B80; 35Q53; 37K05; 37K10Lie algebra; Integrable Hamiltonian system; Curve motions; Planar filament equation; mKdV equation
Keywords: 35Q53; 35B30; 35B44; 35C07; 35G25A two component Novikov system; Besov spaces; Local well-posedness; Blow-up criteria
Keywords: primary; 35Q53; secondary; 35B05; Korteweg-de Vries equation; Weighted Sobolev spaces;
Keywords: Cauchy problem; local well-posedness; Sobolev spaces; bilinear estimate35K30; 35Q53
Keywords: 35Q53; 37K40Camassa–Holm equation; Asymptotic property; Asymptotic density; Momentum density
Keywords: modified Camassa-Holm equation; Cauchy problem; non-uniform continuity; Sobolev spaces35A07; 35B30; 35Q53
Keywords: 35Q53; 35Q80; 35Q55; 35G25Kudryashov method; 3D- Gross–Pitaevskii equation; Solitary wave solutions
Keywords: 93C20; 93B05; 93B07; 35Q53; 35P20; Controllability to trajectories; Viscous Burgers equation; Series of exponentials; Observability; Biorthogonal;
Small data scattering of semirelativistic Hartree equation
Keywords: 35Q55; 35Q53; Semirelativistic Hartree equation; Yukawa type potential; Small data scattering; Angularly averaged Strichartz estimate; Up and Vp spaces;
Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs
Keywords: 35Q51; 35Q53; 37K40; Symbolic computation; Lump solution; Interaction solution;
Nonlinear waves in layered media: Solutions of the KdV-Burgers equation
Keywords: 35Q53; 37K40; Kortweg-de Vries-Burgers equation; Layered media; Soliton; Breather; Asymptotics; Conservation law;
Characterising the path-independent property of the Girsanov density for degenerated stochastic differential equations
Keywords: 60H10; 35Q53; Degenerated stochastic differential equations (SDEs); Girsanov transformation; Non-Lipschitz SDEs with jumps; Semi-linear partial integro-differential equation of parabolic type;
Analyticity of the global attractor for damped forced periodic Korteweg-de Vries equation
Keywords: 35Q53; 37L50; 35B41; Forced damped periodic KdV equations; Global attractor; Gevrey regularity;
Multiple soliton solutions for the (3+1) conformable space-time fractional modified Korteweg-de-Vries equations
Keywords: (3+1) modified Korteweg-de-Vries equations; Conformable fractional derivative; Soliton solutions; 35B35; 35Q53; 76B05;
Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system
Keywords: 35Q53; 37K10; 35B15; Riemann-Hilbert problem; N-soliton solution; Integrable hierarchy;
On the modified KP hierarchy: Tau functions, squared eigenfunction symmetries and additional symmetries
Keywords: 35Q53; 37K10; 37K40; Modified KP hierarchy; Tau functions; Squared eigenfunction symmetries; Additional symmetries;
Asymptotic behavior of Boussinesq system of KdV-KdV type
Keywords: primary; 93B05; 93D15; 35Q53; Boussinesq system KdV-KdV type; Stabilization; Feedback integral transformation; Backstepping method;
Nonexistence of pure multi-solitons for the quartic gBBM equation
Keywords: Nonintegrable; Generalized BBM equation; Pure multi-solitons; Approximate solution; 35Q53; 35C10; 35B35; 35B40;
Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities
Keywords: 35Q53; 35Q72; 49L25; 35F25; 35L40; 35L45; 65M06; 65M12; 65M15; 74H20; 74H25; Hamilton-Jacobi system; Non-local eikonal system; Non-local transport system; BV estimate; Discontinuous viscosity solution; Dislocation dynamics;
Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation
Keywords: 35B10; 35B35; 35P05; 35Q53; 37K45; Periodic traveling waves; Asymptotic stability; Korteweg-de Vries equation; Dispersive estimates;
Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
Keywords: primary; 35Q53; 35B40; secondary; 35B30; Generalized Korteweg-de Vries equation; Scattering problem; Threshold solution;
On the wellposedness of the KdV/KdV2 equations and their frequency maps
Keywords: primary; 37K10; secondary; 35Q53; 35D05; KdV equation; KdV2 equation; Frequency map; Well-posedness; Ill-posedness; Convexity properties of Hamiltonians of integrable PDEs;
Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability
Keywords: 35G20; 35Q53; 37K10; 49S05; 76A60; Generalized higher order NLS equation; Solitary wave solutions; Mathematical Physics methods;
Periodic boundary conditions for KdV-Burgers equation on an interval
Keywords: 35Q53; Kortveg-de Vries-Burgers equation; Initial value-boundary problem; Periodical perturbation; Asymptotics;
On nonlinear superposition of the KdV-Burgers shock waves and the behavior of solitons in a layered medium
Keywords: 35Q53; 37K40; 35B06; KdV-Burgers equation; Nonlinear superposition; Invariant solution; Soliton;
Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs
Keywords: Two variable orthogonal polynomials; 2D Toda lattice; Block Lax pairs; 42C05; 33C50; 35Q53;
The stochastic Korteweg-de Vries equation on a bounded domain
Keywords: Stochastic Korteweg-de Vries equation; Weak martingale solution; Unique Continuation Property; 60H15; 35Q53;
The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrödinger equation and its solutions
Keywords: 35G20; 35Q53; 37K10; 49S05; 76A60; Higher order NLS equation; Generalized higher order of KdV equation; Traveling wave solutions; Mathematical physics methods;
A Nash-Moser-Hörmander implicit function theorem with applications to control and Cauchy problems for PDEs
Keywords: 47J07; 35Q53; 35Q93; Nash-Moser implicit function theorem; Control of PDEs; Quasi-linear PDEs;
On optimal exponential decay properties of solutions to the Korteweg-de Vries Equation
Keywords: primary; 35Q53; secondary; 35B05; Korteweg de Vries equation; Exponential decay; Kato estimates;
Existence of global solutions and global attractor for the third order Lugiato-Lefever equation on T
Keywords: primary; 35Q55; 35Q53; secondary; 35A01; 35B41; Third order Lugiato-Lefever equation; Strichartz' estimate on one dimensional torus; Nonlinear smoothing effect; Global attractor;
Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle
Keywords: 17B68; 35Q53; 37K10; 58J70; Lax-Sato integrability; Heavenly equations; Torus diffeomorphisms; Lie-Poisson structure; Lagrange-d'Alembert principle;
Orbital stability of periodic traveling-wave solutions for the log-KdV equation
Keywords: 76B25; 35Q51; 35Q53; Orbital stability; Log-KdV equation; Periodic waves;
Low regularity for the fifth order Kadomtsev-Petviashvili-I type equation
Keywords: 35E15; 35Q53; Well-posedness; Fifth order Kadomtsev-Petviashvili-I equation; Dyadic Xs,b spaces;