Abstract
Ultra-long waves in the modified Burger model are studied by using the method of travelling-wave solution. Taylor series expansion is used to isolate the characteristics of linear waves and identify the nonlinear waves. The analytical solutions to nonlinear ultra-long waves with the complete Coriolis force and heating，which can be approximately described by the KdV equation and the combined KdV and mKdV （KdV-mKdV） equation，are obtained. The cnoidal waves，solitary waves，and soliton-like solutions are also obtained.
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