×

zbMATH — the first resource for mathematics

On a class of singular nonlinear traveling wave equations. (English) Zbl 1158.35080
A class of singular reaction-diffusion equations is under consideration. The authors study solitons, kink and periodic waves, using methods from the dynamical systems theory. Parametric conditions that guarantee the existence of the the aforementioned solutions are derived and given explicitly.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/S0960-0779(02)00482-4 · Zbl 1030.35120 · doi:10.1016/S0960-0779(02)00482-4
[2] DOI: 10.1007/978-1-4613-8159-4 · doi:10.1007/978-1-4613-8159-4
[3] DOI: 10.1007/978-1-4612-1056-6 · doi:10.1007/978-1-4612-1056-6
[4] DOI: 10.1007/978-1-4612-1140-2 · Zbl 0515.34001 · doi:10.1007/978-1-4612-1140-2
[5] Hirsch M., Lecture Notes in Mathematics 583, in: Invariant Manifolds (1976)
[6] DOI: 10.1016/S0307-904X(00)00031-7 · Zbl 0985.37072 · doi:10.1016/S0307-904X(00)00031-7
[7] DOI: 10.1142/S0252959902000365 · Zbl 1011.35014 · doi:10.1142/S0252959902000365
[8] Li J. B., Int. J. Bifurcation and Chaos 12 pp 3973–
[9] Lopes O., Electron. J. Diff. Eqs. 5 pp 1–
[10] Malaguti L., J. Diff. Eqs. 117 pp 281–
[11] DOI: 10.1007/b98869 · Zbl 1006.92002 · doi:10.1007/b98869
[12] DOI: 10.1007/978-1-4612-0977-5 · doi:10.1007/978-1-4612-0977-5
[13] DOI: 10.1007/978-1-4684-0392-3 · doi:10.1007/978-1-4684-0392-3
[14] DOI: 10.1103/PhysRevLett.70.564 · Zbl 0952.35502 · doi:10.1103/PhysRevLett.70.564
[15] Rosenau P., Phys. Rev. Lett. 73 pp 737–
[16] DOI: 10.1016/S0375-9601(97)00241-7 · Zbl 1052.35511 · doi:10.1016/S0375-9601(97)00241-7
[17] DOI: 10.1016/S0167-2789(98)00148-1 · Zbl 0938.35172 · doi:10.1016/S0167-2789(98)00148-1
[18] DOI: 10.1016/S0375-9601(00)00577-6 · Zbl 1115.35365 · doi:10.1016/S0375-9601(00)00577-6
[19] Sanchez-Gaeduno F., J. Diff. Eqs. 195 pp 471–
[20] Satnoianu R. A., Discr. Contin. Dyn. Syst. Ser. B 1 pp 339–
[21] DOI: 10.1016/S0960-0779(01)00109-6 · Zbl 0997.35083 · doi:10.1016/S0960-0779(01)00109-6
[22] DOI: 10.1016/S0960-0779(03)00059-6 · Zbl 1068.35148 · doi:10.1016/S0960-0779(03)00059-6
[23] DOI: 10.1016/S0960-0779(00)00272-1 · Zbl 1028.35133 · doi:10.1016/S0960-0779(00)00272-1
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.