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Initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov with nonlinerity of higher order are considered.

In 1676, I. Newton, in a letter to the Secretary of the Royal London Society, G. Oldenburg, described an iterative procedure for finding the root of a nonlinear equation, which is known today as Newton's method. Inverse or implicit func-tion theorems are theorems on the existence of a solution to a non-linear equa-tion, and their proofs, based on Newton's method, are natural and transparent.