Точные решения нелинейных телеграфных уравнений с переменными коэффициентами

   Описаны различные классы нелинейных телеграфных уравнений с переменными коэффициентами c(x)u_{n +} d(x)u_{τ =} [a(x)u_x]_x + b(x)u_x + p(x)u_x + p(x)f(u), которые допускают точные решения с функциональным разделением переменных вида u = U(z), z = ϕ , (x,t ).  Показано, что функция источника f(u) и любые четыре из пяти коэффициентов a(x), b(x), c(x),  d(x), p(x) этих уравнений могут быть выбраны произвольно, а оставшийся коэффициент через них выражается. Исследованы свойства и построены некоторые решения переопределенной нелинейной системы дифференциальных уравнений, которым удовлетворяет функция ф(x,t). Приведены примеры конкретных уравнений и их точных решений. Построены также некоторые точные решения типа обобщенной бегущей волны более сложных нелинейных телеграфных уравнений с запаздыванием вида c(x)u_{n +} d(x)u_{τ =} [a(x)u_x]_x + b(x)u_x + p(x)u_x + p(x)f(u, w), w = u(x,t - τ), где τ > 0 – время запаздывания, f (u, w) – произвольная функция двух аргументов.

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