Keywords: Finite-dimensional system; Liouville integrability; Bi-Hamiltonian system; Involutive solutions; Soliton hierarchy; 37K05; 37K10; 35Q53;
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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: 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: 14J70; 15A23; 33C45; 37K10; 37L60; 42C05; 46L55; Darboux transformations; Christoffel transformations; Multivariate orthogonal polynomials; Borel-Gauss factorization; Algebraic varieties; Bivariate product Legendre polynomials;
Keywords: 58D19; 53C42; 37K10; 53A04; Isothermic surfaces; Lie point symmetries; Non-removable parameter; Lax pair; Gauss-Codazzi equations; Clifford algebra;
Keywords: 37K05; 37K10; 37K20; 37K25; Lagrangian representation; Bi-Hamiltonian structure; Hydrodynamic type system; WDVV equations;
Keywords: 35Q51; 37K10; 37K15; 37K40; Harry Dym; Invertible point transformation; High-frequency limit; Multi-phase solutions; Lax pair;
Keywords: 34A34; 34C20; 34C45; 37J30; 37K10; Analytic differential systems; Non-isolated singular point; Local integrability; Invariant manifold;
Keywords: 35B44; 35L05; 37K10; Rod equation; Blow-up; Shallow water;
Keywords: 35Q75; 83C15; 37K05; 37K10; General heavenly equation; Lax pair; Recursion operator; Symplectic form; Hamiltonian operator; Jacobi identities;
Keywords: Higher-order Schrödinger equation; Weak interaction; Soliton perturbation theory; 35Q55; 37K10;
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: Complex integrable dispersionless equation; Hirota method; Pfaffian; Soliton interation35Q53; 37K10; 35C05; 37K40
Keywords: 15A23; 33C45; 37K10; 37L60; 42C05; 46L55; Multivariate orthogonal polynomials; Borel-Gauss factorization; Quasi-determinants; Christoffel-Darboux kernels; Darboux transformations; Christoffel formula; Quasi-tau matrices; Kernel polynomials; Integrable
Keywords: 37K05; 37K10; 37K35Geometry of differential equations; Integrability; Symmetries; Conservation laws; Differential coverings
Keywords: 37K10; 58J70; 35A30; 35G20; 47J35Zero-curvature representations; Spectral parameters; Symmetries; Integrable equations; Jet spaces
Keywords: 33C45; 42C05; 15A23; 37K10; Multiple orthogonal polynomials; Christoffel-Darboux formula; Moment matrices; Jacobi type matrices; Gauss decomposition;
Keywords: primary; 34C25; secondary; 37C27; 37K10; 42A10; 42B05; Harmonic Balance Method; Period function; Hamiltonian potential system; Fourier series;
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: 37K05; 37K10; 37K20; 37K25Hamiltonian operator; Jacobi identity; Projective group; Quadratic complex; Monge metric; Reciprocal transformation
Keywords: 41A21; 41A27; 37K10; 47N20; 42C05; 33D45; 39A13Generalised Zernike polynomials; Rodrigues-type formula; Ordering of Zernike polynomials; Bivariate orthogonal polynomials; Hermite–Zernike polynomials
CK transformations, symmetries, exact solutions and conservation laws of the generalized variable-coefficient KdV types of equations
Keywords: 37K10; 35C05; CK transformation; Lie group classification; Exact solution; Conservation law; Variable-coefficient equation;
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;
Bäcklund transformations for a new extended Painlevé hierarchy
Keywords: Extended Painleváe hierarchy; Bäcklund transformations; 34M55; 37K35; 37K10; 33E17;
DSF chain for biorthogonal polynomials and its application to matrix eigenvalue problems
Keywords: 33D45; 35Q55; 37K10; 37K35; 41A21; 42C05; 65F15; Schur flow; Qd-algorithm; Matrix eigenvalue problems; Numerical algorithms; Integrable systems; Biorthogonal polynomials;
Soliton solutions and eigenfunctions of linearized operator for a higher-order nonlinear Schrödinger equation
Keywords: Partial differential equations; Higher-order Schrödinger equation; Linearization operator; Squared eigenfunctions; Soliton perturbation theory; 35Q55; 37K10;
An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy
Keywords: Soliton hierarchies; Spectral problems; Liouville integrable; Hamiltonian structure; 37K05; 37K10; 35P30; 37K30;
K(m, n) equations with fifth order symmetries and their integrability
Keywords: Symmetries; Integrability; Bi-Hamiltonian structures; Reciprocal transformations; 37K05; 37K10;
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,;
Three-component nonlocal conservation laws for Lax-integrable 3D partial differential equations
Keywords: 35B06; 35G20; 35G50; 37K05; 37K10; Lax-integrable equations; Differential coverings; Nonlocal conservation laws; Bäcklund transformations;
Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations
Keywords: 58H05; 58J70; 35A30; 37K05; 37K10; Exotic cohomology; Lie pseudo-groups; Maurer-Cartan forms; Symmetries of differential equations; Lax representations;
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;
Higher-order rational solutions for a new integrable nonlocal fifth-order nonlinear Schrödinger equation
Keywords: 35Q55; 37K10; Nonlocal nonlinear Schrödinger equation; Lax pair; Darboux transformation; Rational solution;
On a description of the Toda hierarchy using cocycle maps
Keywords: 34L40; 37K10; 47B36; 81Q10; Toda flows; Jacobi operators; Cocycle dynamics;
Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system
Keywords: 35Q53; 37K10; 35B15; Riemann-Hilbert problem; N-soliton solution; Integrable hierarchy;
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;
Phase portraits for some symmetric Riccati cubic polynomial differential equations
Keywords: primary; 37J35; 37K10; Riccati polynomial differential systems; Vector fields; Phase portrait; Reversibility; Equivariance;
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;
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;
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;
Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
Keywords: 37K05; 37K10; 37K20; Multicomponent BKP hierarchy; Dispersionless BKP hierarchy; Additional symmetry; Wâ Lie algebra; Quantum torus algebra; Perturbative quantum torus algebra;
On the Darboux integrability of the logarithmic galactic potentials
Keywords: primary; 37J35; 37K10; Logarithmic galactic potential; Polynomial integrability; Rational integrability; Darboux polynomials; Darboux first integrals; Invariant algebraic hypersurfaces;
Deformed cohomologies of symmetry pseudo-groups and coverings of differential equations
Keywords: 58H05; 58J70; 35A30; 37K05; 37K10; Deformed cohomologies; Lie pseudo-groups; Maurer-Cartan forms; Symmetries of differential equations; Coverings of differential equations;
Möbius-toda hierarchy and its integrability
Keywords: Möbius-Toda equation; soliton solutions; Lax equation; Möbius-Toda hierarchy; tau function; 37K05; 37K10; 37K20;
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;
A new Liouville transformation for the Geng-Xue system
Keywords: Liouville transformation; Bi-Hamiltonian structure; Painlevé property; 37K05; 37K10; 37K35;