Results 51 to 60 of about 3,184 (198)
Hints on the Hirota Bilinear Method
Acta Physica Polonica A, 2007 We discuss four stages of the Hirota bilinear method, for construction of soliton solutions to partial difierential equations: the proper substitution to express the equation in the bilinear variables (1), reduction of the excess degrees of freedom (2), the perturbation scheme (3), and solution of the system of equations at the successive orders of ...
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Hirota Bilinear Method and Relativistic Dissipative Soliton Solutions in Nonlinear Spinor Equations
, 2023 12 pages, talk in III. International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2022), Technical University of Civil Engineering of Bucharest (Romania) 4-7 July ...
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq +4 more
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Advances in Mathematical Physics, 2020 Explicit rational-exponential solutions for the Kadomtsev-Petviashvili-II equation with a self-consistent source (KPIIESCS) are studied by the Hirota bilinear method.
Dan Su +3 more
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Fusion rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds
, 1997 We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota equation). The
Lipan, O., Wiegmann, P. B., Zabrodin, A.
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Two-Dimensional Toda-Heisenberg Lattice [PDF]
, 2013 We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which ...
Vekslerchik, Vadim E.
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Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid +5 more
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Bilinearization of Discrete Soliton Equations and Singularity Confinement
, 1996 Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement.
Grammaticos +14 more
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Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended ...
Abdul Saboor +5 more
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Ain Shams Engineering JournalThis research investigates the extended Kadomtsev-Petviashvili-Boussinesq equation, relevant in numerous scenarios involving dissipative media. To initiate the analysis, a Hirota bilinear form is applied, leading to a Bäcklund transformation for the ...
Nauman Raza +4 more
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