×

zbMATH — the first resource for mathematics

Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method. (English) Zbl 1099.65095
Summary: A combined sine-cosine-Gordon and a double combined sine-cosine-Gordon equations, that combine the effects of sine and cosine, are investigated. The analysis rests mainly on the newly developed variable separated ordinary differential equation method by Sirendaoreji and S. Jiong [Phys. Lett., A 298, No. 2–3, 133–139 (2002; Zbl 0995.35056)]. Exact travelling wave solutions for the combined equations are formally derived by using this method. The work emphasizes the power of the method that can be used in problems of identical nonlinearities.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX Cite
Full Text: DOI
References:
[1] Sirendaoreji, S.; Sun Jiong, S., A direct method for solving sinh-Gordon type equation, Phys. lett. A, 298, 133-139, (2002) · Zbl 0995.35056
[2] Fu, Z.; Liu, S.; Shida Liu, S., Exact solutions to double and triple sinh-Gordon equations, Z. naturforsch., 59a, 933-937, (2004)
[3] Perring, J.K.; Skyrme, T.H., A model unified field equation, Nucl. phys., 31, 550-555, (1962) · Zbl 0106.20105
[4] Whitham, G.B., Linear and nonlinear waves, (1999), Wiley-Interscience New York, NY · Zbl 0373.76001
[5] Infeld, E.; Rowlands, G., Nonlinear waves, solitons and chaos, (2000), Cambridge University Press Cambridge, England · Zbl 0726.76018
[6] Polyanin, A.; Zaitsev, V.F., Handbook of nonlinear partial differential equations, (2004), CRC Boca Raton, FL · Zbl 1053.35001
[7] Ablowitz, M.J.; Herbst, B.M.; Schober, C., On the numerical solution of the sinh-Gordon equation, J. comput. phys., 126, 299-314, (1996) · Zbl 0866.65064
[8] Wei, G.W., Discrete singular convolution for the sinh-Gordon equation, Physica D, 137, 247-259, (2000) · Zbl 0944.35087
[9] Malfliet, W., Solitary wave solutions of nonlinear wave equations, Am. J. phys., 60, 7, 650-654, (1992) · Zbl 1219.35246
[10] Malfliet, W., The tanh method:I. exact solutions of nonlinear evolution and wave equations, Phys. scr., 54, 563-568, (1996) · Zbl 0942.35034
[11] Malfliet, W., The tanh method: II. perturbation technique for conservative systems, Phys. scr., 54, 569-575, (1996) · Zbl 0942.35035
[12] Wazwaz, A.M., The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations, Appl. math. comput., 167, 2, 1196-1210, (2005) · Zbl 1082.65585
[13] Wazwaz, A.M., The tanh method for travelling wave solutions of nonlinear equations, Appl. math. comput., 154, 3, 713-723, (2004) · Zbl 1054.65106
[14] Wazwaz, A.M., Partial differential equations: methods and applications, (2002), Balkema Publishers The Netherlands · Zbl 0997.35083
[15] A.M. Wazwaz, Exact solutions to the combined and the double combined sinh-cosh-Gordon like equations by the tanh method and the variable separated ODE method, Appl. Math. Comput., in press. · Zbl 1096.65104
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.