Results 41 to 50 of about 458,840 (351)
Stability of Periodic Traveling Wave Solutions to the Kawahara Equation
SIAM Journal on Applied Dynamical Systems, 2018 We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of small-amplitude solutions, we show that generalised resonance is a mechanism for high-frequency instabilities.
Olga Trichtchenko +2 more
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Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves [PDF]
Memoirs of the American Mathematical Society, 2020 We prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x x
Berti, M., Montalto, R.
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Elastic and nonelastic interactional solutions for the (2 + 1)-dimensional Ito equation
Arab Journal of Basic and Applied Sciences, 2019 In this paper, based on the bilinear form and two new test functions, for the (2 + 1)-dimensional Ito equation, we obtain non-elastic interactional solutions composed of three different types of waves including the solitary wave, the periodic wave and ...
Ai-Juan Zhou, Lan Lan
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Nonlinear wave equations: constraints on periods and exponential bounds for periodic solutions
Duke Mathematical Journal, 1997 The authors discuss properties of the nonlinear wave equation \(\partial^2_t\varphi= \Delta\varphi+ f(\varphi)\), where \(f\in C^3(\mathbb{R},\mathbb{R})\) satisfies \(f(0)= 0\), while \(t\in (-\infty,+\infty)\) and \(x\in\mathbb{R}^N\). Solutions \(\varphi(x, t)\) are supposed to be periodic in \(t\), and for fixed \(t\) in \(L^2(\mathbb{R}^N)\) with ...
Pyke, R. M., Sigal, I. M.
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Results in Physics, 2022 In this article, we study the generalized (3+1)-dimensional nonlinear wave equation where is investigated in soliton theory and by employing the Hirota’s bilinear method the bilinear form is obtained, and the N-soliton solutions are constructed.
Guiping Shen +5 more
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Periodic solutions of nonlinear wave equations [PDF]
Archive for Rational Mechanics and Analysis, 1983 On obtient des conditions suffisantes pour l'existence de solutions doublement periodiques de l'equation d'onde non lineaire u ts =f(t,s,u), u(t+T,s)=u(t,s)=u(t,s+T) ou f est une fonction continue donnee dans R 3 et f est T-periodique en t et ...
Cesari, Lamberto, Kannan, R.
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Exact solitary and periodic-wave solutions of the K(2,2) equation (defocusing branch)
, 2010 An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the K(2, 2) equation (defocusing branch). Some known results in the literature are recovered more efficiently, and some new exact
Cao, J. +4 more
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Some periodic and solitary travelling-wave solutions of the short pulse equation
, 2008 Exact periodic and solitary travelling-wave solutions of the short pulse equation are ...
Parkes, E.J.
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Collocation schemes for periodic solutions of neutral delay differential equations
, 2005 We introduce two collocation schemes for the computation of periodic solutions of neutral delay differential equations (NDDEs): one based on a direct discretisation of the underlying NDDE, and one based on a discretisation of a related delay differential
Wilson, RE +8 more
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The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations
Journal of Applied Mathematics, 2012 This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the ...
Yadong Shang, Xiaoxiao Zheng
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