Exact solutions for some nonlinear evolution equations which describe pseudo-spherical surfaces

Hamiltonian Structure, Soliton Solution and Conservation Laws for a New Fifth-Order Nonlinear Evolution Equation Which Describes Pseudo-Spherical Surfaces

“…Now, we choose 0 1 , 0 (31) and use (7) and the BT (26); we obtain the new solution class of the new fifth-order evolution Equation (20) From Equations (19) and (22) the first few order Hamiltonians are deter-mined by the relation…”

Travelling Wave Solutions of Kaup-Kupershmidt Equation Which Describes Pseudo Spherical Surfaces

“…The double-kink solutions (19), (20), and (21) are characterized by the eigenvalue 1 µ = (see Figures 1-6). …”

“…We can cite the inverse scattering transform [6], the Bäcklund and Darboux transform [7]- [10], Hirota's bilinear method [11], the homogeneous balance method [12], Jacobi elliptic function method [13], the tanh method and extended tanh-function method [14]- [20], F-expansion method [21]- [23] and so on. The notion of conservation laws is important in the study of nonlinear evolution equations (NLEEs) appearing in mathematical physics [24].…”

Exact Solitary Wave Solutions for the Generalized Schamel Korteweg–De Vries Equation

“…Thus, it is important to investigate the exact explicit solutions of NLEEs. In recent years, various powerful methods have been presented for finding exact solutions of the NLEEs in mathematical physics, such as modified simple equation method (Bhrawy, et al, 2013), extended F-expansion method (Ma, 1993), tanh-sech method (Malfliet, 1992;Khater, et al, 2002;Wazwaz, 2006), extended tanh method (Ma & Fuchssteiner, 1996;El-Wakil & Abdou, 2007;Fan, 2000;Maliet, 2004), sine-cosine method (Wazwaz, 2004 a;Wazwaz, 2004b;Yusufoglu & Bekir, 2006) and Bä cklund transformation (Ma & Lee, 2009;Khater, et al, 2006;Khater, et al, 2004;Sayed, 2013) but solving nonlinear equations is still an important task. Some of the nonlinear models in plasma and dust plasma are described by canonical models, such as the KdV, the mKdV, and so on (Hassan, 2010).…”