Results 51 to 60 of about 1,408 (291)
On the optimal focusing of solitons and breathers in long‐wave models [PDF]
Studies in Applied Mathematics, 2019 AbstractConditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long‐wave models, the classic and the modified Korteweg–de Vries equations.
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Variational methods for breather solutions of nonlinear wave equations
Nonlinearity, 2021 Abstract We construct infinitely many real-valued, time-periodic breather solutions of the nonlinear wave equation ∂ t
Mandel, Rainer, Scheider, Dominic
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Akhmediev breathers and Peregrine solitary waves in a quadratic medium [PDF]
Optics Letters, 2017 We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves, in the regime of cascading second-harmonic generation.
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Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation
Advances in Mathematical Physics, 2022 Most of the papers have explored the interactions between solitons with a zero background, while reports about exact solutions for nonzero background are rare.
Bao Wang, Zhiqiang Chen
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Two-breather solutions for the class I infinitely extended nonlinear Schrodinger equation and their special cases [PDF]
, 2020 We derive the two-breather solution of the class I infinitely extended nonlinear Schrödinger equation. We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free parameters of the two
Akhmediev, Nail, Crabb, Matthew
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Breather Solutions of N-wave Equations
, 2012 We consider $N$-wave type equations related to symplectic and orthogonal algebras. We obtain their soliton solutions in the case when two different $\mathbb{Z}_2$ reductions (or equivalently one $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$-reduction) are imposed.
Gerdjikov, Vladimir, Valchev, Tihomir
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The rogue wave and breather solution of the Gerdjikov-Ivanov equation [PDF]
Journal of Mathematical Physics, 2012 The Gerdjikov-Ivanov (GI) system of q and r is defined by a quadratic polynomial spectral problem with 2 × 2 matrix coefficients. Each element of the matrix of n-fold Darboux transformation (DT) for this system is expressed by a ratio of (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions, which implies the determinant representation ...
Xu, Shuwei, He, Jingsong
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New dynamical behaviors for a new extension of the Shallow water model
Results in Physics, 2022 The aim of this work, is to construct some novel solutions for a new extension of the shallow water model in (3+1)-dimensions. Based on two methods namely; simplified Hirota’s method and a long-wave method a class of solutions are reported.
Jian-Guo Liu +2 more
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, 2020 Hirota’s bilinear method is used in this paper to obtain some breather wave and lumps solutions to the Caudrey–Dodd–Gibbon equation through the symbolic Mathematica 12 package.
Bayram, Mustafa +3 more
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Breathers and rogue waves for semilinear curl-curl wave equations
Journal of Elliptic and Parabolic Equations, 2023 AbstractWe consider localized solutions of variants of the semilinear curl-curl wave equation $$s(x) \partial _t^2 U +\nabla \times \nabla \times U + q(x) U \pm V(x) \vert U \vert ^{p-1} U = 0$$ s ( x )
Michael Plum, Wolfgang Reichel
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