Traveling wave solutions of viscous conservation laws, that are associated to Lax shocks of the inviscid equation, have generically a transversal viscous profile. In the case of a non-transversal viscous profile we show by using Melnikov theory that a parametrized perturbation of the profile equation leads generically to a saddle–node bifurcation of these solutions. An example of this bifurcation in the context of magnetohydrodynamics is given. The spectral stability of the traveling waves generated in the saddle–node bifurcation is studied via an Evans function approach. It is shown that generically one real eigenvalue of the linearization of the viscous conservation law around the parametrized family of traveling waves changes its sign at the bifurcation point. Hence this bifurcation describes the basic mechanism of a stable traveling wave which becomes unstable in a saddle–node bifurcation.

粘性守恒定律的行波解与无粘性方程的松散冲击相关，通常具有横向粘性剖面。在非横向粘性剖面的情况下，我们通过使用 Melnikov 理论表明，剖面方程的参数化扰动通常会导致这些解的鞍点分岔。给出了磁流体动力学背景下这种分叉的一个例子。通过埃文斯函数方法研究了在鞍节点分岔中产生的行波的光谱稳定性。结果表明，围绕参数化行波族的粘性守恒定律线性化的一个实特征值在分岔点处改变其符号。