New exact solutions of the (n+1)-dimensional sine-Gordon equation using double elliptic equation method

In this paper, the (n+1)-dimensional sine-Gordon equation is studied using double elliptic equation method. With the aid of Maple, more exact solutions expressed by Jacobi elliptic functions are obtained. When the modulus m of Jacobi elliptic function is driven to the limit 1 and 0, some exact solutions expressed by hyperbolic function solutions and trigonometric functions can also be obtained, respectively.

[1]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[2]  Bin He,et al.  New exact solutions of the double sine-Gordon equation using symbolic computations , 2007, Appl. Math. Comput..

[3]  Paul Abbott,et al.  The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations , 2002 .

[4]  Deng-Shan Wang,et al.  Further improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equation , 2005 .

[5]  Sen Yang,et al.  The periodic wave solutions for the (3+1)-dimensional Klein-Gordon-Schrodinger equations , 2005 .

[6]  Double elliptic equation method and new exact solutions of the (n+1)-dimensional sinh-Gordon equation , 2007 .

[7]  Zuntao Fu,et al.  Breather solutions and breather lattice solutions to the sine-Gordon equation , 2007 .

[8]  Kongqing Yang,et al.  The extended F-expansion method and exact solutions of nonlinear PDEs , 2004 .

[9]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[10]  Qi Wang.  An application of the modified Adomian decomposition method for (N , 2006, Appl. Math. Comput..

[11]  N. Vitanov.  Breather and soliton wave families for the sine–Gordon equation , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Zuntao Fu,et al.  New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations , 2001 .

[13]  Nikolay K. Vitanov,et al.  On travelling waves and double-periodic structures in two-dimensional sine - Gordon systems , 1996 .

[14]  Mingliang Wang,et al.  Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation , 2005 .

[15]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[16]  Engui Fan,et al.  Using symbolic computation to exactly solve a new coupled MKdV system , 2002 .

[17]  Jibin Li,et al.  Bounded travelling wave solutions for the (n + 1)-dimensional sine- and sinh-Gordon equations , 2005 .

[18]  P. Stevenhagen,et al.  ELLIPTIC FUNCTIONS , 2022 .