Bilinear form and exact solutions for a new extended (2+1)-dimensional Boussinesq equation
Results in Physics, 2021 In this article, a new extended (2+1)-dimensional Boussinesq equation which can be used to describe the propagation of shallow water waves, was investigated.
Ping Cui
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The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source [PDF]
Discrete Dynamics in Nature and Society, 2012 The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property.
Yali Shen, Fengqin Zhang, Xiaomei Feng
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Bilinear Form and Two Bäcklund Transformations for the (3+1)-Dimensional Jimbo-Miwa Equation [PDF]
Abstract and Applied Analysis, 2015 With Bell polynomials and symbolic computation, this paper investigates the (3+1)-dimensional Jimbo-Miwa equation, which is one of the equations in the Kadomtsev-Petviashvili hierarchy of integrable systems.
He Li, Yi-Tian Gao
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Robust bilinear rotations II [PDF]
Magnetic ResonanceBilinear rotations are essential building blocks in modern NMR spectroscopy. They allow the rotation of an isolated spin without couplings (i.e., bilinear interactions) in one way, while rotating spins with a matched coupling in another way.
Y. T. Woordes, B. Luy
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On Backlund transformations and identities in bilinear form [PDF]
Journal of Physics A: Mathematical and General, 1990 Summary: For bilinear equations of the form \(P(D)f\cdot f=0\) we find all possibilities for rewriting \(g^ 2P(D)f\cdot f-f^ 2P(D)g\cdot g=0\) in the form \(Q(D)f\cdot g=0\). This is the first step in finding a Bäcklund transformation.
Post, Gerhard F.
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Bilinear form of the regularized long wave equation and its multi-soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 We consider utmost significant model, namely, the regularized long-wave equation involving dispersion and weedy nonlinearity effects that arises in the nonlinear dynamics of phonon packets in crystals, shallow water, plasma and ion acoustic waves.
Mohammad Mobarak Hossain +2 more
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Soliton solutions by means of Hirota bilinear forms
Partial Differential Equations in Applied Mathematics, 2022 The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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ON THE POTENTIALITY OF A CLASS OF OPERATORS RELATIVE TO LOCAL BILINEAR FORMS
Ural Mathematical Journal, 2021 The inverse problem of the calculus of variations (IPCV) is solved for a second-order ordinary differential equation with the use of a local bilinear form.
Svetlana A. Budochkina +1 more
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The soliton solutions for semidiscrete complex mKdV equation [PDF]
ITM Web of Conferences, 2020 The semidiscrete complex modified Korteweg–de Vries equation (semidiscrete cmKdV), which is the second member of the semidiscrete nonlinear Schrődinger hierarchy (Ablowitz–Ladik hierarchy), is solved using the Hirota bilinear formalism.
Babalic Corina N.
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A Multi-Timescale Bilinear Model for Optimization and Control of HVAC Systems with Consistency
Energies, 2021 Reducing the energy consumption of the heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is of both academic and practical significance.
Zelin Nie, Feng Gao, Chao-Bo Yan
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