Results 31 to 40 of about 394 (186)
Advances in Mathematical Physics, 2015 The relations between Dp-operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with Dp-operators of nonlinear equations directly and quickly.
Jingzhu Wu, Xiuzhi Xing, Xianguo Geng
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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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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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Mixed Lump-Stripe Soliton Solutions to a New Extended Jimbo-Miwa Equation
Advances in Mathematical Physics, 2023 In this paper, the localized properties of lump and interaction solutions to a new extended Jimbo-Miwa (EJM) equation are studied. Based on the Hirota bilinear method and the test function method, the exact solutions of the EJM equation are discussed ...
Yinghui He
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Journal of Mathematics, Volume 2026, Issue 1, 2026.The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects.
Fei Li +4 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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Q-soliton solution for two-dimensional q-Toda lattice
Қарағанды университетінің хабаршысы. Физика сериясы, 2019 The Toda lattice is a non-linear evolution equation describing an infinite system of masses on a line that interacts through an exponential force. The paper analyzes the construction of soliton solution for the q-Toda lattice in the two-dimensional case.
Б.Б. Кутум, Г.Н. Шайхова
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