1. Typically, a modified Newton's method is used to solve these nonlinear equations . 2. Nonlinear equations model the dependence of phase velocity on amplitude, replacing by.3. Gradient descent can also be used to solve a system of nonlinear equations . 4. For a description of linear and nonlinear equations , see " linear equation ". 5. A system of coupled nonlinear equations can be solved iteratively by Newton's method. 6. Linear differential equations frequently appear as approximations to nonlinear equations . 7. These nonlinear equations must be solved numerically with the appropriate boundary and initial conditions. 8. Iterative methods are often the only choice for nonlinear equations . 9. These nonlinear equations describe the classical wave limit of a system of interacting identical particles. 10. This nonlinear equation has some rich properties, especially in terms of existence of unique solutions.