  In the process of the deep learning, we integrate more integrable information
of nonlinear wave models, such as the conservation law obtained from the
integrable theory, into the neural network structure, and propose a
conservation-law constrained neural network method with the flexible learning
rate to predict solutions and parameters of nonlinear wave models. As some
examples, we study real and complex typical nonlinear wave models, including
nonlinear Schr\"odinger equation, Korteweg-de Vries and modified Korteweg-de
Vries equations. Compared with the traditional physics-informed neural network
method, this new method can more accurately predict solutions and parameters of
some specific nonlinear wave models even when less information is needed, for
example, in the absence of the boundary conditions. This provides a reference
to further study solutions of nonlinear wave models by combining the deep
learning and the integrable theory.
