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Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/(sici)1097-0312(199908)52:8<949::aid-cpa3>3.0.co;2-dopenalex-snapshot
A shallow water equation on the circle
inferredcites →https://doi.org/10.1006/aima.1998.1768openalex-snapshot
Acoustic Scattering and the Extended Korteweg– de Vries Hierarchy
inferredcites →https://doi.org/10.1006/jdeq.1999.3683openalex-snapshot
Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
inferredcites →https://doi.org/10.1007/978-3-540-69969-9openalex-snapshot
Hamiltonian Methods in the Theory of Solitons
inferredcites →https://doi.org/10.1007/978-3-642-88703-1_4openalex-snapshot
The Symmetry Approach to Classification of Integrable Equations
inferredcites →https://doi.org/10.1007/978-94-007-1023-8_8openalex-snapshot
Nonlocal Symmetries and Ghosts
inferredcites →https://doi.org/10.1007/bf00049574openalex-snapshot
Applications of lie groups to differential equations
inferredcites →https://doi.org/10.1007/bf01017819openalex-snapshot
Lie-algebraic approach to nonlocal symmetries of integrable systems
inferredcites →https://doi.org/10.1007/bf02102436openalex-snapshot
Surfaces on Lie groups, on Lie algebras, and their integrability
inferredcites →https://doi.org/10.1007/s00220-005-1356-zopenalex-snapshot
On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation
inferredcites →https://doi.org/10.1016/0167-2789(81)90004-xopenalex-snapshot
Symplectic structures, their Bäcklund transformations and hereditary symmetries
inferredcites →https://doi.org/10.1016/0167-2789(94)90093-0openalex-snapshot
On a completely integrable nonlinear hyperbolic variational equation
inferredcites →https://doi.org/10.1016/0167-2789(95)00133-oopenalex-snapshot
On a class of physically important integrable equations
inferredcites →https://doi.org/10.1016/0167-2789(96)00048-6openalex-snapshot
Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
inferredcites →https://doi.org/10.1016/0550-3213(79)90517-0openalex-snapshot
Soliton equations and pseudospherical surfaces
inferredcites →https://doi.org/10.1016/s0375-9601(01)00070-6openalex-snapshot
On the initial value problem for a completely integrable shallow water wave equation
inferredcites →https://doi.org/10.1017/s0956792500000188openalex-snapshot
Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
inferredcites →https://doi.org/10.1023/a:1010774630016openalex-snapshot
Some Geometric Aspects of Integrability of Differential Equations in Two Independent Variables
inferredcites →https://doi.org/10.1023/a:1014933316169openalex-snapshot
Geometric Integrability of the Camassa–Holm Equation
inferredcites →https://doi.org/10.1063/1.527974openalex-snapshot
New classes of symmetries for partial differential equations
inferredcites →https://doi.org/10.1063/1.531486openalex-snapshot
Zero curvature formulations of dual hierarchies
inferredcites →https://doi.org/10.1063/1.533284openalex-snapshot
Conservation laws and Calapso–Guichard deformations of equations describing pseudo-spherical surfaces
inferredcites →https://doi.org/10.1080/00036810108840938openalex-snapshot
Inverse scattering solutions of the hunter-saxton equation
inferredcites →https://doi.org/10.1088/0305-4470/25/15/014openalex-snapshot
New nonlocal symmetries with pseudopotentials
inferredcites →https://doi.org/10.1090/s0894-0347-03-00421-1openalex-snapshot
Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
inferredcites →https://doi.org/10.1103/physrevlett.71.1661openalex-snapshot
An integrable shallow water equation with peaked solitons
inferredcites →https://doi.org/10.1103/physrevlett.87.194501openalex-snapshot
An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion
inferredcites →https://doi.org/10.1137/050623036openalex-snapshot
Global Solutions of the Hunter--Saxton Equation
inferredcites →https://doi.org/10.1142/9789812817587_0044openalex-snapshot
NON-LOCAL BÁCKLUND TRANSFORMATIONS FOR HARRY DYM AND KORTEWEG-DE VRIES EQUATIONS
inferredcites →https://doi.org/10.1143/ptp.105.77openalex-snapshot
On the Relation between Lie Symmetries and Prolongation Structures of Nonlinear Field Equations: Non-Local Symmetries
inferredcites →https://doi.org/10.14492/hokmj/1381517775openalex-snapshot
Pseudopotentials and symmetries of evolution equations
inferredcites →https://doi.org/10.48550/arxiv.math/9808130openalex-snapshot
Homological Methods in Equations of Mathematical Physics
inferredcites →https://doi.org/10.48550/arxiv.solv-int/9606004openalex-snapshot
Symmetries of KdV and Loop Groups
inferredcites →https://doi.org/10.5802/aif.1757openalex-snapshot
Existence of permanent and breaking waves for a shallow water equation: a geometric approach
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/978-1-4939-2950-4_13openalex-snapshot
Local Isometric Immersions of Pseudo-Spherical Surfaces and Evolution Equations
inferred← citeshttps://doi.org/10.1007/s00025-011-0167-0openalex-snapshot
Equations of Pseudo-Spherical Type (After S.S. Chern and K. Tenenblat)
inferred← citeshttps://doi.org/10.1007/s00033-013-0339-8openalex-snapshot
Algebro-geometric solutions for the Hunter–Saxton hierarchy
inferred← citeshttps://doi.org/10.1007/s00332-024-10097-5openalex-snapshot
Local Isometric Immersions and Breakdown of Manifolds Determined by Cauchy Problems of the Degasperis–Procesi Equation
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Non-local symmetries, consistent Riccati expansion solvability and analytic solutions for the generalised Broer–Kaup system
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Residual Symmetry and Interaction Solutions of the (2+1)-Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation
inferred← citeshttps://doi.org/10.1007/s44198-025-00365-7openalex-snapshot
On a Generalized Camassa–Holm Equation Describing Pseudospherical Surfaces
inferred← citeshttps://doi.org/10.1016/j.asej.2023.102214openalex-snapshot
Numerous explicit soliton solutions to the fractional simplified Camassa-Holm equation through two reliable techniques
inferred← citeshttps://doi.org/10.1016/j.geomphys.2012.03.011openalex-snapshot
The modified Hunter–Saxton equation
inferred← citeshttps://doi.org/10.1016/j.jde.2010.05.016openalex-snapshot
Fifth-order evolution equations describing pseudospherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2014.06.010openalex-snapshot
Fourth order evolution equations which describe pseudospherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2016.02.015openalex-snapshot
Second order evolution equations which describe pseudospherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2019.11.069openalex-snapshot
A class of quasilinear second order partial differential equations which describe spherical or pseudospherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2022.08.017openalex-snapshot
On a class of systems of hyperbolic equations describing pseudo-spherical or spherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2023.09.028openalex-snapshot
Breakdown of pseudospherical surfaces determined by the Camassa-Holm equation
inferred← citeshttps://doi.org/10.1016/j.jde.2023.10.032openalex-snapshot
A class of third order quasilinear partial differential equations describing spherical or pseudospherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2025.02.003openalex-snapshot
Systems of differential equations of higher order describing pseudo-spherical or spherical surfaces
inferred← citeshttps://doi.org/10.1016/j.jmaa.2016.09.044openalex-snapshot
Local isometric immersions of pseudospherical surfaces described by evolution equations in conservation law form
inferred← citeshttps://doi.org/10.1016/j.padiff.2024.100932openalex-snapshot
Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach
inferred← citeshttps://doi.org/10.1016/s0034-4877(25)00036-9openalex-snapshot
A Moving Curve Description of The Hunter–Saxton Equation
inferred← citeshttps://doi.org/10.1023/b:acap.0000035588.67805.0bopenalex-snapshot
Reducibility of Zero Curvature Representations with Application to Recursion Operators
inferred← citeshttps://doi.org/10.1080/14029251.2018.1452669openalex-snapshot
Nonlocal symmetries of Plebański’s second heavenly equation
inferred← citeshttps://doi.org/10.1088/1742-6596/3264/1/012015openalex-snapshot
Partial Differential Equations and Surface Theory
inferred← citeshttps://doi.org/10.1088/1751-8113/40/17/004openalex-snapshot
On nonlocal symmetries of some shallow water equations
inferred← citeshttps://doi.org/10.1098/rspa.2023.0670openalex-snapshot
Existence and uniqueness of periodic pseudospherical surfaces emanating from Cauchy problems
inferred← citeshttps://doi.org/10.1111/sapm.12457openalex-snapshot
A Novikov equation describing pseudo‐spherical surfaces, its pseudo‐potentials, and local isometric immersions
inferred← citeshttps://doi.org/10.1142/s0219199716500218openalex-snapshot
Third-order differential equations and local isometric immersions of pseudospherical surfaces
inferred← citeshttps://doi.org/10.1142/s0219199718500256openalex-snapshot
Local isometric immersions of pseudo-spherical surfaces and kth order evolution equations
inferred← citeshttps://doi.org/10.1142/s0219887813500461openalex-snapshot
NONLOCAL SYMMETRIES, COMPACTON EQUATIONS, AND INTEGRABILITY
inferred← citeshttps://doi.org/10.1142/s1402925112500258openalex-snapshot
On the Nonlocal Symmetries of the μ-Camassa–Holm Equation
inferred← citeshttps://doi.org/10.1155/2011/738509openalex-snapshot
Geometric Integrability of Some Generalizations of the Camassa‐Holm Equation
inferred← citeshttps://doi.org/10.14445/22315373/ijmtt-v56p534openalex-snapshot
A Comparative Analysis of DTM and HAM Solutions for Hunter-Saxton Equation and Fisher Equation
inferred← citeshttps://doi.org/10.22533/at.ed.996230510openalex-snapshot
Some contributions to the study of evolution equations describing pseudospherical surfaces, and the theory of zero-curvature representations
inferred← citeshttps://doi.org/10.48550/arxiv.1207.0574openalex-snapshot
The algebro-geometric solutions for Hunter-Saxton hierarchy
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Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions
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