(3+1)-Dimensional Nonlinear Equations and Couplings of Fifth-Order Equations in the Solitary Waves Theory: Multiple Soliton Solutions
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Solitons appear as a result of a balance between a weakly nonlinear convection and a linear dispersion. The soliton is a localized highly stable wave that retains its identity – shape and speed – upon interaction and resembles particle-like behavior. It is a localized solitary wave so that it decays or approaches a constant at infinity. In the case of a collision, solitons undergo a phase shift. The stability of solitons stems from the delicate equilibrium between the two effects of nonlinearity and dispersion.
Types of Traveling Waves
Traveling waves appear in many scientific and engineering applications in solitary wave theory. Solitons, kinks, peakons, cuspons, compactons, negatons, positons, complexitons, and others are examples of solitary waves. Solitons are localized wave packets which are asymptotically zero at large distances with exponential wings or tails. Kink waves are solitons that rise or descend from one asymptotic state to another, and hence another...
- Wazwaz AM (2009a) Adomian decomposition method applied to nonlinear evolution equations in solitons theory. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, HeibelbergGoogle Scholar
- Wazwaz AM (2011a) Multi-front waves for extended form of modified Kadomtsev–Petviashvili equation. Appl Math Mech 32(7):875–880Google Scholar
- Wazwaz AM (2011b) Distinct kinds of multiple soliton solutions for a (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation. Phys Scr 84:055006Google Scholar
- Wazwaz AM (2011c) A new fifth order nonlinear integrable equation: multiple soliton solutions. Physica Scripta 83:015012Google Scholar
- Wazwaz AM (2011d) A new generalized fifth-order nonlinear integrable equation. Phys Scr 83:035003Google Scholar
Books and Reviews
- Drazin PG, Johnson RS (1996) Solitons: an introduction. Cambridge University Press, CambridgeGoogle Scholar
- Wazwaz AM (2002) Partial differential equations: methods and applications. Balkema Publishers, LisseGoogle Scholar
- Wazwaz AM (2009b) Partial differential equations: methods and solitary waves theory. Springer/HEP, Berlin/BeijingGoogle Scholar
- Wazwaz AM (2011e) Linear and nonlinear integral equations. Springer/HEP, Berlin/BeijingGoogle Scholar