Abstract
New solitary and extended wave solutions of the generalized sinh-Gordon (SHG) equation with a variable coefficient are found by utilizing the self-similar transformation between this equation and the standard SHG equation. Two arbitrary self-similar functions are included in the known solutions of the standard SHG equation, to obtain exact solutions of the generalized SHG equation with a specific variable coefficient. Our results demonstrate that the solitary and extended waves of the variable-coefficient SHG equation can be manipulated and controlled by a proper selection of the two arbitrary self-similar functions.
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