### The Riccati Equation Mapping Method for Solving Nonlinear Partial Differential Equations in Mathematical Physics

#### Abstract

doi:10.14456/WJST.2014.14

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WM Zhang and LX Tian. An extended tanh-method and its application to the soliton breaking equation. J. Phys. Conf. Ser. 2008; 96, 012069.

CQ Dai and YZ Ni. Novel interactions between semi-foldons of the (2+1)-dimensional Boiti-Leon-Pempinelli equation. Phys. Scr. 2006; 74, 584.

CL Zheng, LQ Chen and JF Zheng. Peakon, compacton and loop excitatations with periodic behavior in Kdv type models related to Schrödinger system. Phys. Lett. A 2005; 340, 397-402.

S Tsuchiya, F Dalfovo and L Pitaevskii. Solitons in two-dimensional Bose-Einstein condensates. Phys. Rev. A 2008; 77, 045601.

JP Gollub and MC Cross. Nonlinear dynamics: Chaos in space and time. Nature 2000; 404, 710-1.

CL Zheng, GP Cai and JY Qiang. Chaos, solitons and fractals in (2+1)-dimensional KdV system derived from a periodic wave solution. Chaos Soliton. Fract. 2007; 34, 1575-83.

JP Fang, CL Zheng and JM Zhu. New variable separation excitations, rectangle like solitons and fractal solitons in the Boiti-Leon-Pempinelli system. Acta Phys. Sin. 2005; 54, 2990-3006.

CL Zheng, JP Fang and LQ Chen. Bell-like and peak-like loop solitons in (2+1)-dimensional Boiti-Leon-Pempinelli system. Acta Phys. Sin. 2005; 54, 1468-508.

SD Zhu. The generalizing Riccati equation mapping method in nonlinear evolution equation: application to (2+1)-dimensional Boiti-Leon-Permpinelle equation. Chaos Soliton. Fract. 2008; 37, 1335-42.

HY Ruan and YX Chen. Study on solitons interaction in the (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Acta Phys. Sin. 2003; 52, 1313-406.

ZY Ma and CL Zheng. Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation. Chin. Phys. 2006; 15, 45-108.

CQ Dai and YZ Ni. Novel interactions between solitons of the (2+1)-dimensional dispersive long wave equation. Chaos, Soliton. Fract. 2008; 37, 269-77.

SH Ma, QB Ren, JP Fang and CL Zheng. Special soliton structures and the phenomena of fission and annihilation of solitons for the (2+1)-dimensional Broer-Kaup system with variable coefficients. Acta Phys. Sin. 2007; 57, 6777-807.

JF Zhang, WH Ruang and CL Zheng. Coherent soliton structures of a new (2+1)-dimensional evolution equation. Acta Phys. Sin. 2002; 52, 2676-707.

SH Ma, JP Fang and QB Ren. New mapping solutions and localized structures for the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system. Acta Phys. Sin. 2007; 56, 6784-807.

SH Ma, XH Wu, JP Fang and CL Zheng. New exact solutions and special soliton structures for the (3+1)-dimensional Burgers system. Acta Phys. Sin. 2008; 57, 11-7.

SH Ma, JP Fang and HP Zhun. Dromion soliton waves and the their evolution in the background of Jacobi sine waves. Acta Phys. Sin. 2007; 56, 4319-407.

ZY Ma. The projective Riccati equation expansion method and variable-separation solutions for the nonlinear physical differential equation in physics. Chin. Phys. 2007; 16, 1848-54.

A Huber. A note on a class of solitary -like solutions of the Tzitzéica equation generated by a similarity reduction. Phys. D: Nonlinear Phenom. 2008; 237, 1079-87.

CL Bai, XQ Liu and H Zhao. New localized excitations in a (2+1)-dimensional Broer-Kaup system, Chin. Phys. 2005; 14, 285-92.

BG Konopelcheno and VG Dubrovsky. Some new integrable nonlinear evolution equation in (2+1)-dimensions. Phys. Lett. A 1984; 102, 15-7.

A Maccart. A new integrable Davey-Stewartson -type equation. J. Math. Phys.1999; 40, 3971-7.

Z Jiang and RK Sullough. Combined ã and Riemann-Hilbert inverse methods for integrable nonlinear evolution equations in (2+1)-dimensions. J. Phys. A: Math. Gen. 1987; 20, L429-L435.

J Lin, SY Lou and KL Wang. Multi-soliton solutions of the Konopelchenko-Dubrovsky equation. Chin. Phys. Lett. 2001; 18, 1173-5.

A Bekir. Applications of the extended tanh-method for coupled nonlinear evolution equations. Commun. Nonlinear Sci. Numer. Simulat. 2008; 13, 1748-57.

DS Wang and HQ Zhang. Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation. Chaos Soliton. Fract. 2005; 25, 601-10.

LN Song and HQ Zhang. New exact solutions for Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation. Appl. Math. Comput. 2007; 187, 1373-88.

AM Wazwaz. New kinks and solitons solutions to the (2+1)-dimensional Konopelchenko-Dubrovsky equation. Math. Comput. Model 2007; 45, 473-9.

S Zhang. Symbolic computation and new families of exact non-traveling wave solutions of (2+1)-dimensional Konopelchenko-Dubrovsky equations. Chaos Soliton. Fract. 2007; 31, 951-9.

S Zhang. The periodic wave solutions for the (2+1)-dimensional Konopelchenko-Dubrovsky equations. Chaos Soliton. Fract. 2006; 36, 1213-20.

TC Xia, ZS Lü and HQ Zhang. Symbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrovsky equations. Chaos Soliton. Fract. 2004; 20, 561-6.

B Zheng. Exact solutions for two nonlinear equations. WSEAS Trans. Math. 2010; 9, 458-67.

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