数展开法[4—6], 试探函数法[7, 8], 非线性变换法[9, 10] 和sine2cosine 方法[11]. 文献[15, 17,
18, 20] 也探讨了非线性方程的解. 但是, 这些方法只能求得非线性波方程的冲击波解和孤波解 …

A Jacobi elliptic function expansion method, which is more general than the hyperbolic
tangent function expansion method, is proposed to construct the exact periodic solutions of …

New Jacobi elliptic functions are applied in Jacobi elliptic function expansion method to
construct the exact periodic solutions of nonlinear wave equations. It is shown that more new …

In this paper, we devise a new unified algebraic method to construct a series of explicit exact
solutions for general nonlinear equations. Compared with most existing methods such as …

非线性波动方程的准确解对理解非线性方程的性质有很大的帮助, 特别对于非线性方程的数值解
来说, 解析解有助于验证数值解的正确性, 因此, 求解非线性方程的解析解在非线性问题中占有 …

A new direct and unified algebraic method for constructing multiple travelling wave solutions
of general nonlinear evolution equations is presented and implemented in a computer …

In this paper, by introducing new approach, the improved tan (ϕ (ξ)/2)-expansion method
(ITEM) is further extended into Gerdjikov–Ivanov (GI) model. As a result, the hyperbolic …

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3× 3 Lax
pair. The Darboux transformations with the nonzero plane-wave solutions are presented to …

随着科学技术的发展, 非线性在自然科学和社会科学领域的作用越来越重要,
对于非线性问题的关注也越来越大. 在非线性问题中, 对非线性演化方程的求解和定性分析占有 …

为了理解各种非线性问题的物理机理, 各种非线性模型(非线性方程) 被陆续提了出来. 一般而言,
很难得到这些非线性方程的准确解析解, 因此, 更多地得到的是应用计算方法得到的数值解 …