Kirchgässner, Klaus Wave-solutions of reversible systems and applications. (English) Zbl 0507.35033 J. Differ. Equations 45, 113-127 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 123 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs Keywords:wave-solutions; reversible systems; homoclinic solutions; waves in channels; one parameter-family of semilinear elliptic equations; Dirichlet-boundary conditions; decay to zero at infinity; solitary waves; density stratified channels with an inviscid fluid; center-manifold; existence; uniqueness PDFBibTeX XMLCite \textit{K. Kirchgässner}, J. Differ. Equations 45, 113--127 (1982; Zbl 0507.35033) Full Text: DOI References: [1] S. Chow and J. K. Hale, Bifurcation theory, manuscript.; S. Chow and J. K. Hale, Bifurcation theory, manuscript. · Zbl 0487.47039 [2] Kirchgässner, K.; Scheurle, J., On the bounded solutions of a semilinear equation in a strip, J. Differential Equations, 22, 119-148 (1979) · Zbl 0372.35034 [3] Kirchgässner, K.; Scheurle, J., Bifurcation from the continuous spectrum and singular solutions, (Knops, R., Trends in Applications of Pure Mathematics to Mechanics, Vol. III (1980), Pitman: Pitman London), 138-154 [4] Kirchgässner, K.; Scheurle, J., Bifurcation of non-periodic solutions of some semilinear equations in unbounded domains, (Amann, H.; Bazley, N.; Kirchgässner, K., Applications of Nonlinear Analysis in the Physical Sciences, Vol. 6 (1981), Pitman: Pitman London), 41-59 [5] Kopell, N.; Howard, L. N., Bifurcations and trajectories joining critical points, Adv. in Math., 18, 306-358 (1975) · Zbl 0361.34026 [6] Long, R. R., Some aspects of the flow of stratified fluids. I. A theoretical investigation, Tellus, 5, 42-57 (1953) [7] Moser, J., Stable and Random Motions in Dynamical Systems (1973), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J [8] M. Renardy, Bifurcation of singular and transient solutions spatially nonperiodic patterns for chemical reaction models in infinitely extended domains, in “Contributions to Nonlinear Partial Differential Equations” (H. Berestycki and H. Brézis, Eds.), Pitman, London, in press.; M. Renardy, Bifurcation of singular and transient solutions spatially nonperiodic patterns for chemical reaction models in infinitely extended domains, in “Contributions to Nonlinear Partial Differential Equations” (H. Berestycki and H. Brézis, Eds.), Pitman, London, in press. · Zbl 0482.34036 [9] Ter-Krikorov, A. M., Théorie exacte des ondes longues stationnaires dans un liquide hétèrogène, J. Mécanique, 2, 351-376 (1963) [10] R. E. L. Turner, Internal waves in fluids with rapidly varying density, manuscript.; R. E. L. Turner, Internal waves in fluids with rapidly varying density, manuscript. · Zbl 0514.76019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.