# The integral Cauchy problem for generalized Boussinesq equations with general leading parts

## TL;DR

This paper investigates the initial value problems for generalized Boussinesq equations with various differential operators, establishing existence, uniqueness, and regularity of solutions, and analyzing different types of these equations.

## Contribution

It introduces a unified approach to study the regularity and solution properties of Boussinesq equations with general differential operators.

## Key findings

- Existence and uniqueness of solutions are proven.
- Regularity properties depend on the choice of differential operators.
- The framework applies to various types of Boussinesq equations.

## Abstract

In this paper, the integral initial value problems for Boussinesq type equations are studied. The equation include the general differential operators. The existence, uniqueness and regularity properties of solution of these problems are obtained. By choosing differential operators including in the equation, the regularity properties of the Cauchy problem for different type of Boussinesg equations are studied.