Results 51 to 60 of about 9,595 (205)
Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof [PDF]
, 2017 In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation $u""+\beta u" + e^u-1=0$ for all parameter values $\beta \in [0.5,1.9]$.
Berg, Jan Bouwe van den +3 more
core +4 more sources
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most ...
Raffaele Folino +2 more
wiley +1 more source
Dissipative periodic and chaotic patterns to the KdV--Burgers and Gardner equations [PDF]
, 2019 We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems and Shil'nikov's analysis.
Adams, Ronald, Mancas, Stefan C.
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Generalized homoclinic solutions for the Swift–Hohenberg equation
Journal of Mathematical Analysis and Applications, 2012 The authors study the Swift-Hohenberg equation, which depends on one parameter and describes the onset of the Rayleigh-Bénard heat convection. By giving an explicit construction, they prove the existence of a homoclinic solution connecting a periodic orbit for every positive parameter.
Deng, Shengfu, Li, Xiaopei
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer +2 more
wiley +1 more source
The Swift-Hohenberg equation with a nonlocal nonlinearity [PDF]
, 2013 It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional
Dawes, Jonathan H. P., Morgan, David
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Multiple front and pulse solutions in spatially periodic systems
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
wiley +1 more source
Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit [PDF]
, 2013 We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it.
Grébert, Benoît +2 more
core +2 more sources
Homoclinic solutions for second order discrete p-Laplacian systems [PDF]
Advances in Difference Equations, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He, Xiaofei, Chen, Peng
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Multiple solutions of nonlinear boundary value problems with oscillatory solutions
Mathematical Modelling and Analysis, 2006 We consider two second order autonomous differential equations with critical points, which allow the detection of an exact number of solutions to the Dirichlet boundary value problem.
S. Ogorodnikova, F. Sadyrbaev
doaj +1 more source