Found 3,878 Documents (Results 1–100)
Numerical inverse scattering transform for the derivative nonlinear Schrödinger equation. (English) Zbl 07916679
Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries. (English) Zbl 07915228
Soliton condensates for the focusing nonlinear Schrödinger equation: a non-bound state case. (English) Zbl 07912357
Investigation of space-time dynamics of Akbota equation using Sardar sub-equation and Khater methods: unveiling bifurcation and chaotic structure. (English) Zbl 07909673
Gauge equivalence of \(1+1\) Calogero-Moser-Sutherland field theory and a higher-rank trigonometric Landau-Lifshitz model. (English. Russian original) Zbl 07908857
Theor. Math. Phys. 219, No. 3, 1004-1017 (2024); translation from Teor. Mat. Fiz. 219, No. 3, 545-561 (2024).
A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics. (English. Russian original) Zbl 07908852
Theor. Math. Phys. 219, No. 3, 933-943 (2024); translation from Teor. Mat. Fiz. 219, No. 3, 462-473 (2024).
Group analysis and invariant solutions of the \((3+1)\)-dimensional defocusing Gardner-KP equation. (English) Zbl 07903719
Exotic localized waves in the higher-order nonlinear Schrödinger equation with nonvanishing boundary conditions. (English) Zbl 07903697
Painlevé analysis of the resonant third-order nonlinear Schrödinger equation. (English) Zbl 07901114
Comment on: “Integrability, modulational instability and mixed localized wave solutions for the generalized nonlinear Schrödinger equation”. (English) Zbl 07900954
Superposed and superposed-type double periodic Jacobi elliptic function solutions of variable coefficients KdV equation. (English) Zbl 07898335
Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation. (English) Zbl 07895064
Riemann-Hilbert problem associated with an integrable generalized mixed nonlinear Schrödinger equation. (English) Zbl 07893733
Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation. (English) Zbl 07888721
Painlevé analysis, bilinear forms, Bäcklund transformations and solitons for a variable-coefficient extended Korteweg-de Vries equation with an external-force term in fluid mechanics and plasma dynamics. (English) Zbl 07888033
A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problem. (English) Zbl 07887691
Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles. (English) Zbl 07881040
Solitary wave solutions in \((2+1)\) dimensions: the KdV equation derived from ideal fluid models. (English) Zbl 07879198
Real reduced matrix mKdV integrable hierarchies under two local group reductions. (English) Zbl 07878409
The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class. (English) Zbl 07877943
Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime. (English) Zbl 07875588
Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation. (English) Zbl 07873700
Stability of smooth periodic traveling waves in the Degasperis-Procesi equation. (English) Zbl 07873558
Dynamics of general soliton and rational solutions in the \((3+1)\)-dimensional nonlocal Mel’nikov equation with non-zero background. (English) Zbl 07871722
The intertwined derivative Schrödinger system of Calogero-Moser-Sutherland type. (English) Zbl 07870842
Extensions of dark KdV equations: nonhomogeneous classifications, bosonizations of fermionic systems and supersymmetric dark systems. (English) Zbl 07868593
Dynamical behaviors of various multi-solutions to the (2+1)-dimensional Ito equation. (English) Zbl 07867889
KP reductions and various soliton solutions to the Fokas-Lenells equation under nonzero boundary condition. (English) Zbl 07867796
Parity-time symmetric solitons of the complex KP equation. (English. Russian original) Zbl 1541.37082
Theor. Math. Phys. 219, No. 2, 770-780 (2024); translation from Teor. Mat. Fiz. 219, No. 2, 274-286 (2024).
Classification of the two-component Benjamin-Ono systems. (English. Russian original) Zbl 1541.37077
Theor. Math. Phys. 219, No. 1, 638-662 (2024); translation from Teor. Mat. Fiz. 219, No. 1, 124-150 (2024).
Cauchy problem for a nonlinear Schrödinger equation with a large initial gradient in the weakly dispersive limit. (English. Russian original) Zbl 07864570
Theor. Math. Phys. 219, No. 1, 531-538 (2024); translation from Teor. Mat. Fiz. 219, No. 1, 3-11 (2024).
Reviewer: Hajer Bahouri (Paris)
Extended Lie method for mixed fractional derivatives, unconventional invariants and reduction, conservation laws and acoustic waves propagated via nonlinear dispersive equation. (English) Zbl 07864137
Global energy conservation solution for the \(N - a b c\) family of Camassa-Holm type equation. (English) Zbl 07862783
Conservation laws, modulation instability, and mixed semi-rational solutions for a three-component modified nonlinear Schrödinger equation. (English) Zbl 07861259
Dispersive shock wave structure analysis for the defocusing Lakshmanan-Porsezian-Daniel equation. (English) Zbl 07858933
A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations. (English) Zbl 07858927
Interactions of certain localized waves for an extended \((3+1)\)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics. (English) Zbl 07858889
Semiclassical WKB problem for the non-self-adjoint Dirac operator with a multi-humped decaying potential. (English) Zbl 07856624
Type \((\lambda^\ast,\lambda)\) reduced nonlocal integrable AKNS equations and their soliton solutions. (English) Zbl 07856325
Orbital stability of periodic traveling waves in the \(b\)-Camassa-Holm equation. (English) Zbl 07855420
Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space. (English) Zbl 1540.35363
Instability of \(H^1\)-stable periodic peakons for the higher-order \(\mu\)-Camassa-Holm equation. (English) Zbl 1540.35339
Geometric realization of the Sasa-Satsuma equation on the symmetric space \(\mathrm{SU}(3)/\mathrm{U}(2)\). (English) Zbl 07851956
On the global well-posedness of the Calogero-Sutherland derivative nonlinear Schrödinger equation. (English) Zbl 1539.35226
On the well-posedness of the Cauchy problem for the two-component peakon system in \(C^k \cap W^{k,1}\). (English) Zbl 1540.35118
Bäcklund transformations of multi-component Boussinesq and Degasperis-Procesi equations. (English) Zbl 07850804
Long-time asymptotics for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation with decaying initial value data. (English) Zbl 07850554
Inverse scattering and soliton dynamics for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation. (English) Zbl 07850553
An extended Merola-Ragnisco-Tu lattice integrable hierarchy and infinite conservation laws. (English) Zbl 07850525
Ill-posedness of the Novikov equation in the critical Besov space \(B^1_{\infty, 1}(\mathbb{R})\). (English) Zbl 1539.35218
Exploring accurate soliton propagation in physical systems: a computational study of the (1+1)-dimensional \(\mathbb{MNW}\) integrable equation. (English) Zbl 07846886
Riemann-Hilbert approach and multiple arbitrary-order pole solutions for the Lakshmanan-Porsezian-Daniel equation with finite density initial data. (English) Zbl 07845338
Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation. (English) Zbl 1537.37095
New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation. (English) Zbl 1537.35306
The Dbar-dressing method for the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. (English) Zbl 1537.37088
Quasi-periodic breathers and rogue waves to the focusing Davey-Stewartson equation. (English) Zbl 1541.35393
Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation. (English. Russian original) Zbl 1539.37077
Theor. Math. Phys. 218, No. 3, 388-410 (2024); translation from Teor. Mat. Fiz. 218, No. 3, 449-474 (2024).
A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation. (English. Russian original) Zbl 1539.37074
Theor. Math. Phys. 218, No. 3, 370-387 (2024); translation from Teor. Mat. Fiz. 218, No. 3, 430-448 (2024).
A generalized sine-Gordon equation: reductions and integrable discretizations. (English) Zbl 07839653
Interior inverse problem for global conservative multipeakon solutions of the Camassa-Holm equation. (English) Zbl 07839389
A nonlocal finite-dimensional integrable system related to the nonlocal nonlinear Schrödinger equation hierarchy. (English) Zbl 07838363
Nonlocal Kundu-Eckhaus equation: integrability, Riemann-Hilbert approach and Cauchy problem with step-like initial data. (English) Zbl 1537.35145
Bogoyavlensky-modified KdV hierarchy and toroidal Lie algebra \(\mathrm{sl}^{\mathrm{tor}}_2\). (English) Zbl 07837887
Geometrical correspondence of the Miura transformation induced from affine Kac-Moody algebras. (English) Zbl 07836559
Existence of global solutions to the nonlocal Schrödinger equation on the line. (English) Zbl 1539.35249
Sharp well-posedness for the cubic NLS and mKdV in \(H^s(\mathbb{R})\). (English) Zbl 1540.35372
Reviewer: Guido Schneider (Stuttgart)
A partial-integrable numerical simulation scheme of the derivative nonlinear Schrödinger equation. (English) Zbl 1540.35373
Evolution of initial discontinuities in a particular case of two-step initial problem for the defocusing complex modified KdV equation. (English) Zbl 1536.35259
Physics-informed neural networks with two weighted loss function methods for interactions of two-dimensional oceanic internal solitary waves. (English) Zbl 07827316
Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space. (English) Zbl 1537.35312
Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations. (English) Zbl 07818452
Integrability propagation for a Boltzmann system describing polyatomic gas mixtures. (English) Zbl 1534.35281
Higher-order heat equation and the Gelfand-Dickey hierarchy. (English) Zbl 07813039
Reviewer: Irina V. Konopleva (Ul’yanovsk)
Nonlocal Yajima-Oikawa system: binary Darboux transformation, exact solutions and dynamic properties. (English) Zbl 1534.35376
On the linearizable initial-boundary value problems for the Sasa-Satsuma equation on the half-line. (English) Zbl 1534.35279
The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation. (English) Zbl 1533.35295
Inverse scattering transform for the coupled modified complex short pulse equation: Riemann-Hilbert approach and soliton solutions. (English) Zbl 1533.35325
Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation. (English) Zbl 1533.35304
Analytical properties of nonlinear partial differential equations. With applications to shallow water models. (English) Zbl 07808162
CMS/CAIMS Books in Mathematics 10. Cham: Springer (ISBN 978-3-031-53073-9/hbk; 978-3-031-53076-0/pbk; 978-3-031-53074-6/ebook). xviii, 309 p. (2024).
Reviewer: Dimitar A. Kolev (Sofia)
MSC:
35Q35
35-02
76-02
76B15
76B25
76D05
37K10
37K15
37K35
35A20
35B06
68W30
35C08
35C07
82D55
35R35
34M55
35Q53
35Q55
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