Nonlinear science is one of the greatest discoveries of the 20th century, which has revolutionized our understanding of deterministic problems. As pointed out by Nobel laureate Heisenberg, “the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations ... and therefore we can learn by comparing different nonlinear problems.” However, existing methods for solving nonlinear problems are often limited by the lack of a closed-form expansion for nonlinear terms. As a result, these methods are primarily effective for handling weakly nonlinear cases. Consequently, a unified and effective method for solving strongly nonlinear problems has yet to be established. This work primarily introduces a wavelet-based method for solving nonlinear problems, proposed by the presenter and his research group in recent years. This method exhibits closed-form characteristics for expanding and solving nonlinear terms, thereby achieving unified solutions from weakly nonlinear to strongly nonlinear regimes. Quantitative results obtained from solving typical problems in nonlinear solid mechanics, fluid mechanics, physics, and mathematics demonstrate the advantages of this method, including high accuracy and low computational cost.