A new type of bounded waves for Degasperis–Procesi equation

New exact solutions for two nonlinear equations

“…Eqs. (1.3) and (1.4) have been studied in many literatures successively, for instance [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Since Eqs.…”

Classification of travelling waves in the Fornberg–Whitham equation

“…It is well known that the travelling wave solutions of nonlinear partial differential equations play an important role in explaining some particular physical phenomena. Many powerful methods, such as the auxiliary equation method [20], the general elliptic equation method [21], the F-expansion method [22], the bifurcation theory of the planar dynamical system [23][24][25][26][27] and many others have been successfully used to search for travelling wave solutions. By using those methods many travelling wave solutions under some parametric conditions have been derived, including some special nonsmooth wave solutions, such as looped waves and peaked waves.…”

Exact wave solutions for a class of single-species model of population dynamics

“…As far as we know, it is applied by Li and Liu (2000) for the first time, then followed by many good results (Long, Rui and He, 2005;Li et al, 2006;He et al, 2008;Rui et al, 2008;Chen et al, 2015;Chen and Tang, 2006) and references therein. However, there exists a premise condition in the above applications of this method, namely the dispersive equation can be transformed into an integrable planar system via certain travelling-wave solution ansatz, and more to obtain a integrable system is usually challenging, because there is no fixed method confirming us to find integrable conditions or its first integrals for a general planar system.…”