zbMATH — the first resource for mathematics

High-frequency soliton-like waves in a relaxing medium. (English) Zbl 0946.35094
Summary: A nonlinear evolution equation is suggested to describe the propagation of waves in a relaxing medium. It is shown that in the low-frequency approach this equation is reduced to the KdVB equation. The high-frequency perturbations are described by a new nonlinear equation. This equation has ambiguous looplike solutions. It is established that a dissipative terrn, with a dissipation parameter less than some limit value, does not destroy these looplike solutions.

35Q53 KdV equations (Korteweg-de Vries equations)
74A25 Molecular, statistical, and kinetic theories in solid mechanics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Full Text: DOI
[1] DOI: 10.1063/1.1664873 · Zbl 0283.35020
[2] DOI: 10.1088/0305-4470/25/15/025 · Zbl 0754.35132
[3] DOI: 10.1088/0305-4470/26/22/040 · Zbl 0809.35086
[4] DOI: 10.1051/anphys:0198400902021100
[5] DOI: 10.1088/0305-4470/26/23/047 · Zbl 0824.76008
[6] Yasnikov G. P., J. Eng. Phys. 35 pp 872– (1978)
[7] DOI: 10.1103/PhysRevLett.17.996
[8] Kudryashov N. A., Sov. Phys. Dokl. 34 pp 798– (1989)
[9] DOI: 10.1143/JPSJ.50.1025
[10] DOI: 10.1017/S0022112072002307 · Zbl 0237.76010
[11] DOI: 10.1063/1.523453 · Zbl 0351.35019
[12] Burgers J. M., Adv. Mech. 1 pp xxx– (1948)
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.