Results 11 to 20 of about 636 (179)
Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R. Osborne
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New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation
Abstract and Applied Analysis, 2014 A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and ...
Changfu Liu +3 more
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Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Shock and Vibration, 2016 The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen +2 more
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Homoclinic Solutions of Hamiltonian Systems with Symmetry
Journal of Differential Equations, 1999 Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
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Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems
Abstract and Applied Analysis, 2013 This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a ...
Jingli Xie, Zhiguo Luo, Guoping Chen
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On Existence of Infinitely Many Homoclinic Solutions
Monatshefte f�r Mathematik, 2000 Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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Existence and multiplicity of homoclinic solutions for a difference equation
Electronic Journal of Differential Equations, 2020 The aim of this article is to obtain homoclinic solutions for a discrete problem involving p-Laplacian. We prove the existence of at least one, two and three solutions for the problem. Our approach is based on variational methods. For more information see https://ejde.math.txstate.edu/Volumes/2020/115/abstr ...
SHAPOUR HEIDARKHANI +2 more
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Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation
Abstract and Applied Analysis, 2014 A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed.
Hanlin Chen, Zhenhui Xu, Zhengde Dai
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
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Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems
Abstract and Applied Analysis, 2013 We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
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