Аналитические решения модифицированного уравнения Кортевега – де Вриза – Бюргерса с нелинейным источником

В работе исследуется обобщенное уравнение модифицированного уравнения Кортевега – де Вриза – Бюргерса с нелинейным источником в виде полинома третьей степени. Задача Коши для этого уравнения не решается методом обратной задачи рассеяния. Однако уравнение допускает преобразования сдвига по независимым переменным, поэтому аналитические решения уравнения  ищутся используя переменные бегущей волны. Для того чтобы выяснить возможность существования общего решения нелинейного обыкновенного дифференциального уравнения, на первом этапе исследования применяется тест Пенлеве. Ограничения на параметры математической модели найдены как необходимые условия интегрируемости нелинейного обыкновенного дифференциального уравнения. Учитывая значения индексов Фукса находятся два первых интеграла нелинейного обыкновенногоо дифференциального уравнения третьего порядка. Общее решение уравнения с тремя произвольными постоянными выражено через эллиптическую функцию Якоби. Метод простейших уравнений используется, чтобы найти аналитические решения с одной и двумя произвольными постоянными.

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