Exact solutions of systems describing interacting populations with low critical densities

Kudryashov, 2005, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, 24, 1217, 10.1016/j.chaos.2004.09.109 Kudryashov, 2007, Polygons of differential equations for finding exact solutions, Chaos, Solitons and Fractals, 33, 1480, 10.1016/j.chaos.2006.02.012 Kudryashov, 2008, Solitary and periodic solutions of the generalized Kuramoto–Sivashinsky equation, Regular and Chaotic Dynamics, 13, 234, 10.1134/S1560354708030088 Kudryashov, 2008, Be careful with the Exp-function method, Communications in Nonlinear Science and Numerical Simulation Kudryashov, 2008, Extended simplest equation method for nonlinear differential equations, Applied Mathematics and Computation, 25, 396, 10.1016/j.amc.2008.08.019 Lou, 1991, Exact solitary waves in a convecting fluid, Journal of Physics A: Mathematical and General, 24, L587, 10.1088/0305-4470/24/11/003 Kudryashov, 1996, Solitary waves in active-dissipative dispersive media, Journal of Physics A: Mathematical and General, 29, 8067, 10.1088/0305-4470/29/24/029 Fan, 2000, Extended tanh-function method and its applications to nonlinear equations, Physics Letters, Section A: General, Atomic and Solid State Physics, 277, 212, 10.1016/S0375-9601(00)00725-8 Elwakil, 2002, Modified extended tanh-function method for solving nonlinear partial differential equations, Physics Letters, Section A: General, Atomic and Solid State Physics, 299, 179, 10.1016/S0375-9601(02)00669-2 Liu, 2001, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Physics Letters, Section A: General, Atomic and Solid State Physics, 289, 69, 10.1016/S0375-9601(01)00580-1 Yan, 2003, The extended jacobian elliptic function expansion method and its application in the generalized Hirota–Satsuma coupled KdV system, Chaos, Solitons and Fractals, 15, 575, 10.1016/S0960-0779(02)00145-5 Kudryashov, 1990, Exact solutions of the generalized Kuramoto–Sivashinsky equation, Physics Letters, Section A: General, Atomic and Solid State Physics, 147, 287, 10.1016/0375-9601(90)90449-X Porubov, 1993, Exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid, Journal of Physics A: Mathematical and General, 26, 797, 10.1088/0305-4470/26/17/008 Bazykin, 2003 Skellam, 1991, Random dispersal in theoretical populations, Bulletin of Mathematical Biology, 53, 135, 10.1007/BF02464427 Riznichenko, 2002 Riznichenko, 2004 Estevez, 1990, Painleve analysis of the generalized Burgers–Huxley equation, Journal of Physics A: Mathematical and General, 23, 4831, 10.1088/0305-4470/23/21/023 Yefimova, 2004, Exact solutions of the Burgers–Huxley equation, Journal of Applied Mathematics and Mechanics, 68, 413, 10.1016/S0021-8928(04)00055-3 Kudryashov, 2004 Pearl, 1930