In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = ( κu+ γu ) xx + uuxxxx + μuxxtt + αuxuxxx + βu 2 xx , (1) where α, β, γ, κ and μ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further ...

Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of ...

We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: L(l, p) = ∫ ( 1 2φxφt − (φx) l(l−1) + α(φx) (φxx) 2 ) dx, where the usual fields u(x, t) of the generalized KdV equation are defined by u(x, t) = φx(x, t). For p an arbitrary continuous parameter 0 < p ≤ 2, l = p + 2 we find compacton solutions to these equations which have the feature that their width is indepen...

in this paper , the quintic b-spline collocation scheme is employed to approximate numerical solution of the kdv-like rosenau equation . this scheme is based on the crank-nicolson formulation for time integration and quintic b-spline functions for space integration . the unconditional stability of the present method is proved using von- neumann approach . since we do not know the exact solution...