Search

We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM) equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H¹ (ℝ) energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution. [ABSTRACT FROM AUTHOR]

We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3, 2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the modified Camassa–Holm equation is Painlevé integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation. [ABSTRACT FROM AUTHOR]