This paper presents a new completely integrable dispersive shallow water equation that is biHamiltonian and possesses an infinite number of conservation laws in involution. The equation is derived from Euler's equations using an asymptotic expansion in the Hamiltonian for shallow water dynamics. The equation is: $$ u_{t}+\kappa u_{x}-u_{x x t}+3u u_{x}=2u_{x}u_{x x}+u u_{x x x}, $$ where $ u $ is the fluid velocity, $ \kappa $ is a constant related to the critical shallow water wave speed. This equation retains higher-order terms in a small amplitude expansion of incompressible Euler's equations for unidirectional wave motion. Dropping these terms leads to the Benjamin-Bona-Mahoney (BBM) or Korteweg-de Vries (KdV) equations. The new equation possesses soliton solutions whose limiting form as $ \kappa \rightarrow 0 $ have peaks where first derivatives are discontinuous, known as "peakons." These peakons dominate the solution of the initial value problem for this equation with $ \kappa = 0 $. The equation is biHamiltonian, meaning it can be expressed in Hamiltonian form in two different ways. The ratio of its two Hamiltonian operators is a recursion operator that generates an infinite sequence of conservation laws. This biHamiltonian property allows the equation to be recast as a compatibility condition for a linear isospectral problem, enabling the solution of the initial value problem via the inverse scattering transform (IST) method. The equation is derived by considering the Green-Naghdi (GN) equations and making a unidirectional approximation by relating the momentum density $ m $ to $ \eta $ in the GN system. This leads to the Hamiltonian form of the equation, which is then expanded in terms of a small parameter $ \alpha $. The resulting equation is a BBM equation extended by retaining higher-order terms in an asymptotic expansion in terms of $ \alpha $. The equation is shown to have a biHamiltonian structure, with two Hamiltonian operators $ B_1 = \partial - \partial^3 $ and $ B_2 = \partial m + m \partial $, which form a Hamiltonian pair. The equation is thus biHamiltonian and has an infinite number of conservation laws recursively related to each other. The recursion operator $ R = B_2 B_1^{-1} $ generates a hierarchy of commuting flows, with the first few flows including the original equation and an extension of the integrable Dym equation. The equation is also shown to be isospectral, meaning it has a discrete spectrum and is completely integrable. The isospectral problem is solved using the inverse scattering transform, and the initial value problem is solved by the purely linear IST technique. Numerical simulations confirm the analysis and demonstrate the robustnessThis paper presents a new completely integrable dispersive shallow water equation that is biHamiltonian and possesses an infinite number of conservation laws in involution. The equation is derived from Euler's equations using an asymptotic expansion in the Hamiltonian for shallow water dynamics. The equation is: $$ u_{t}+\kappa u_{x}-u_{x x t}+3u u_{x}=2u_{x}u_{x x}+u u_{x x x}, $$ where $ u $ is the fluid velocity, $ \kappa $ is a constant related to the critical shallow water wave speed. This equation retains higher-order terms in a small amplitude expansion of incompressible Euler's equations for unidirectional wave motion. Dropping these terms leads to the Benjamin-Bona-Mahoney (BBM) or Korteweg-de Vries (KdV) equations. The new equation possesses soliton solutions whose limiting form as $ \kappa \rightarrow 0 $ have peaks where first derivatives are discontinuous, known as "peakons." These peakons dominate the solution of the initial value problem for this equation with $ \kappa = 0 $. The equation is biHamiltonian, meaning it can be expressed in Hamiltonian form in two different ways. The ratio of its two Hamiltonian operators is a recursion operator that generates an infinite sequence of conservation laws. This biHamiltonian property allows the equation to be recast as a compatibility condition for a linear isospectral problem, enabling the solution of the initial value problem via the inverse scattering transform (IST) method. The equation is derived by considering the Green-Naghdi (GN) equations and making a unidirectional approximation by relating the momentum density $ m $ to $ \eta $ in the GN system. This leads to the Hamiltonian form of the equation, which is then expanded in terms of a small parameter $ \alpha $. The resulting equation is a BBM equation extended by retaining higher-order terms in an asymptotic expansion in terms of $ \alpha $. The equation is shown to have a biHamiltonian structure, with two Hamiltonian operators $ B_1 = \partial - \partial^3 $ and $ B_2 = \partial m + m \partial $, which form a Hamiltonian pair. The equation is thus biHamiltonian and has an infinite number of conservation laws recursively related to each other. The recursion operator $ R = B_2 B_1^{-1} $ generates a hierarchy of commuting flows, with the first few flows including the original equation and an extension of the integrable Dym equation. The equation is also shown to be isospectral, meaning it has a discrete spectrum and is completely integrable. The isospectral problem is solved using the inverse scattering transform, and the initial value problem is solved by the purely linear IST technique. Numerical simulations confirm the analysis and demonstrate the robustness