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Multi-shock and soliton solutions of the Burgers equation employing Darboux transformation with the help of the Lax pair
The purpose of this article is to derive a class of multi-soliton solutions of the Burgers equation employing Darboux transformation with the help of...
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Lax pair, conservation laws, breather-to-soliton transitions and modulation instability for a coupled extended modified Korteweg-de Vries system in a fluid
The modified Korteweg-de Vries-type equations can be used to describe the interfacial waves in a fluid, elastic quasi-plane waves in a lattice, and...
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Lax integrability and infinite superposition solutions of a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation
In this article, a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is studied, which is an extended shallow water wave model in the higher...
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In an inhomogeneous multicomponent optical fiber: Lax pair, generalized Darboux transformation and vector breathers for a three-coupled variable-coefficient nonlinear Schrödinger system
Optical fibers are used in the optical sensors, optical imaging, ultrafast lasers and high-speed remote communications. In this paper, a...
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Lax pair, solitons, breathers and modulation instability of a three-component coupled derivative nonlinear Schrödinger system for a plasma
Plasmas are of current interest, supporting some nonlinear phenomena. In this paper, we investigate a three-component coupled derivative nonlinear...
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Discrete Integrable Systems and Random Lax Matrices
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate...
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Continuous limit, higher-order rational solutions and relevant dynamical analysis for Belov–Chaltikian lattice equation with 3\(\times \)3 Lax pair
Belov–Chaltikian (BC) lattice equation, which is related to the research of lattice analogues of W -algebras, is under consideration in this work....
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On the Riemann–Hilbert problem of the matrix Lakshmanan–Porsezian–Daniel system with a \(4\times4\) AKNS-type matrix Lax pair
AbstractThe initial-boundary value problems for the matrix Lakshmanan–Porsezian–Daniel system are studied by utilizing the Fokas unified...
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Lax pair, interactions and conversions of the nonlinear waves for a (2+1)-dimensional nonlinear Schrödinger equation in a Heisenberg ferromagnetic spin chain
Spin waves, the collective excitations of the electron spin systems in the ferromagnetic metals, are used in the telecommunication systems and...
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Lax Pairs for the Discrete Reduced Nahm Systems
We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the Kahan–Hirota–Kimura discretisation procedure. We show that...
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Rogue wave patterns to the artificial synchronization of three uncoupled Ablowitz−Ladik systems in the framework of Babalic−Cârstea auxiliary Lax representation
The artificial synchronization of three uncoupled Ablowitz−Ladik systems associated with the sixth-order auxiliary linear problem is investigated...
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Rational Lax Matrices from Antidominantly Shifted Extended Yangians: BCD Types
Generalizing Frassek et al. (Adv. Math. 401 , 108283 (2022). https://doi.org/10.1016/j.aim.2022.108283 ), we construct a family of SO (2 r ), Sp (2 r ),
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Solitonic interactions and asymptotic analysis for a pair-transition-coupled nonlinear Schrödinger system in an isotropic optical medium
Recently, a pair-transition-coupled nonlinear Schrödinger system, which illustrates the orthogonally-polarized optical waves in an isotropic optical...
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W-Algebras via Lax Type Operators
W-algebras are certain algebraic structures associated to a finite-dimensional Lie algebra...
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Explicit solutions of the Schamel–KdV equation employing Darboux transformation
The aim of this paper is to derive a class of soliton solutions of the Schamel–KdV (SKdV) equation employing Darboux transformation with the help of...
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Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs
AbstractBy including spectral functions, we obtain nonlocal symmetries equivalent to Lie point symmetries of the corresponding extended systems...
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Localized wave solutions of a higher-order short pulse equation
Constructing suitable Lax pair and making use of zero-curvature equation, a higher-order short pulse equation is researched and proved to be Lax...
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Integrable coupled massive Thirring model with field values in a Grassmann algebra
A coupled massive Thirring model of two interacting Dirac spinors in 1 + 1 dimensions with fields taking values in a Grassmann algebra is introduced,...