Solitary Wave Solutions of the Variable Coefficient KdV Burgers Equation
Abstract
In this paper, we nd exact solitary wave solutions for the variablecoefficient KdV Burgers equation of the form ut+uux+f(t)uxx+g(t)uxxx = 0. We construct a transformation of variables which is applied in order to obtain a constant coefficient KdV Burgers equation and also we obtain certain solitary wave solutions with a constraint on f(t) and g(t).
References
[1] M. L. Wang. Solitary wave solutions for variant Boussinesq equations, Physics Letters A, 199(3-4)(1995), 169-172.
[2] M. L. Wang. Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A, 216(1-5)(1996), 67-75.
[3] E. J. Parkes and B. R. Duffy. Travelling solitary wave solutions to a compound KdV-Burgers equation, Physics Letters A, 229(4)(1997), 217-220.
[4] B. R. Duffy and E. J. Parkes. Travelling solitary wave solutions to a seventh-order generalized KdV equation, Physics Letters A, 214(5-6)(1996), 271-272.
[5] Z. T. Fu, S. K. Liu, S. Liua and Q. Zhaoa. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Physics Letters A, 290(1-2)(2001), 72-76.
[6] E.J. Parkesa, B.R. Duffya and P.C. Abbottb. The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations, Physics Letters A, 295(5-6)(2002), 280-286.
[7] D. J. Benney. Long waves on liquid films, Studies in Appl. Math., 45(1-4)(1966), 150-155.
[8] R. S. Johnson. Shallow water waves on a viscous
uid-the undular bore, Phys. of Fluids, 15(10)(1972), 1693-1699.
[9] L. V. Wijngaarden. One-dimensional flow of liquids containing small gas bubbles, Ann. Rev. Fluid Mech., 4(1972), 369-373.
[10] R. S. Johnson. A nonlinear equation incorporating damping and dispersion, J. Fluid Mech., 42(1)(1970), 49-60.
[11] H. Grad and P. N. Hu. Unified shock profile in plasma, Phys. Fluids, 10(12)(1967), 2596-2602.
[12] P. N. Hu. Collisional theory of shock and nonlinear waves in a plasma, Phys. Fluids, 15(5)(1972), 854-864.
[13] G. Gao. A theory of interaction between dissipation and dispersion of turbulance, Sci. China Math., 28(6)(1985), 616-627.
[14] A. J. M. Jawad, M. D. Petkovic and A. Biswas. Soliton solutions of Burgers equations and perturbed Burgers equation, Appl. Math. Comput., 216(11)(2010), 3370-3377.
[2] M. L. Wang. Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A, 216(1-5)(1996), 67-75.
[3] E. J. Parkes and B. R. Duffy. Travelling solitary wave solutions to a compound KdV-Burgers equation, Physics Letters A, 229(4)(1997), 217-220.
[4] B. R. Duffy and E. J. Parkes. Travelling solitary wave solutions to a seventh-order generalized KdV equation, Physics Letters A, 214(5-6)(1996), 271-272.
[5] Z. T. Fu, S. K. Liu, S. Liua and Q. Zhaoa. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Physics Letters A, 290(1-2)(2001), 72-76.
[6] E.J. Parkesa, B.R. Duffya and P.C. Abbottb. The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations, Physics Letters A, 295(5-6)(2002), 280-286.
[7] D. J. Benney. Long waves on liquid films, Studies in Appl. Math., 45(1-4)(1966), 150-155.
[8] R. S. Johnson. Shallow water waves on a viscous
uid-the undular bore, Phys. of Fluids, 15(10)(1972), 1693-1699.
[9] L. V. Wijngaarden. One-dimensional flow of liquids containing small gas bubbles, Ann. Rev. Fluid Mech., 4(1972), 369-373.
[10] R. S. Johnson. A nonlinear equation incorporating damping and dispersion, J. Fluid Mech., 42(1)(1970), 49-60.
[11] H. Grad and P. N. Hu. Unified shock profile in plasma, Phys. Fluids, 10(12)(1967), 2596-2602.
[12] P. N. Hu. Collisional theory of shock and nonlinear waves in a plasma, Phys. Fluids, 15(5)(1972), 854-864.
[13] G. Gao. A theory of interaction between dissipation and dispersion of turbulance, Sci. China Math., 28(6)(1985), 616-627.
[14] A. J. M. Jawad, M. D. Petkovic and A. Biswas. Soliton solutions of Burgers equations and perturbed Burgers equation, Appl. Math. Comput., 216(11)(2010), 3370-3377.
Downloads
Published
2017-03-10
Issue
Section
Чланци