## On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV equations.(English)Zbl 1069.35080

Summary: An algebraic method is devised to construct new exact wave soliton solutions for two generalized nonlinear Hirota-Satsuma coupled KdV systems of partial differential equations using symbolic software like Mathematica or Maple in terms of $$sn(x)-cn(x)$$ Jacobic elliptic functions and $$\sec_q-\tanh_q$$ $$q$$-deformed hyperbolic functions based on the idea of the homogeneous balance method.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

### Software:

Maple; Mathematica
Full Text:

### References:

 [1] Akhiezer, N.I., Elements of theory of elliptic functions, (1990), American Mathematical Society Providence, RI · Zbl 0694.33001 [2] Cao, D.B., Phys. lett. A, 296, 27-33, (2002) [3] Fan, E.G., Phys. lett. A, 282, 18-22, (2001) [4] Fan, E.G.; Hon, B.Y.C., Phys. lett. A, 929, 335-337, (2002) [5] Pu, Z.; Liu, S.; Liu, S., Phys. lett. A, 299, 507-512, (2002) [6] Hon, Y.C.; Fan, E.G., Chaos, solitons & fractals, 19, 515-525, (2004) [7] Li, B.; Chan, Y.; Zhang, H., J. phys. A: math. gen., 35, 8253-8265, (2002) [8] Cheng, L.B., Phys. lett. A, 288, 191-195, (2002) [9] Liu, X.-Q.; Song, J., Phys. lett. A, 298, 253-258, (2002) [10] Satsuma, J.; Hirota, R., J. phys. soc. jpn., 51, 3390-3397, (1982) [11] Wu, Y.T.; Geng, X.G.; Hu, X.B.; Zhu, S.M., Phys. lett. A, 255, 259-264, (1999) [12] Yan, Z., J. phys. A: math. gen., 35, 9923-9930, (2002) · Zbl 1040.35103
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