Continuous solutions of a polynomial-like iterative equation with variable coefficients

The C1 Solutions of the Series-Like Iterative Equation with Variable Coefficients

where F is a given function, f is an unknown function, λi ∈ R i 1, 2, . . . , n , and f k 1, 2, . . . , n is the kth iterate of f, that is, f0 x x, f x f ◦ fk−1 x . The case of all constant λis was considered in 1–10 . In 2000, W. N. Zhang and J. A. Baker first discussed the continuous solutions of such an iterative equation with variable coefficients λi λi x which are all continuous in interva...

The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients

Backlund Transformation and N-soliton-like Solutions to the Combined KdV-Burgers Equation with Variable Coefficients

Abstract: In this paper, through a new transformation, the combined KdvBurgers equation with variable coefficients(vcKdvB) is reduced to a new simplified equation.Based on the homogeneous balance principle(HBP),we studied the Backlund transformation(BT) and several exact soliton-like solutions to this vcKdvB equation. Including single kink-like solitary wave solutions, double-soliton-like solut...