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Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. (English) Zbl 1125.35401
Summary: The solitary wave solutions of the approximate equations for long water waves, the coupled KdV equations and the dispersive long wave equations in $$2 + 1$$ dimensions are constructed by using a homogeneous balance method.

##### MSC:
 35Q51 Soliton equations 35Q53 KdV equations (Korteweg-de Vries equations) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35A35 Theoretical approximation in context of PDEs
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##### References:
 [1] Whitham, G.B., (), 6 [2] Broer, L.T.F., Appl. sci. res., 31, 377, (1975) [3] Kupershmidt, B.A., Comm. math. phys., 99, 51, (1985) [4] Hirota, R.; Satsuma, J., Phys. lett. A, 85, 407, (1981) [5] Dodd, R.; Frody, A., Phys. lett. A, 89, 168, (1982) [6] Oevel, W., Phys. lett. A, 94, 404, (1983) [7] Lu, B.Q., Phys. lett. A, 189, 25, (1994) [8] Boiti, M., Inverse probl., 3, 371, (1987) [9] Paquin, G.; Winternitz, P., Physica D, 46, 122, (1990) [10] Lou, S., Phys. lett. A, 176, 96, (1993) [11] Sachs, R.L., Physica D, 30, 1, (1988) [12] Wang, M., Phys. lett. A, 199, 169, (1995) [13] M. Wang, submitted to Phys. Lett. A.
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