How can we compute the "N-wave" source-solution of the conservation law $$u_t + (u - u^2)_x = 0 \ ?$$

Note: For the case of the Burgers equation $$u_t + (u^2)_x = 0$$ the computation of N-wave solutions is in equation (2.1) of the paper

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057.

But I don't see how to extend this computation to the model above in the question.

How can we compute the "N-wave" source-solution of the conservation law $$u_t + (u - u^2)_x = 0, $$ that is, the entropy solution of this conservation law with the initial data $u(0,\cdot) = (q -p) \delta$, where $\delta$ is the Dirac mass in $0$ and $0 <p, q$?

Note: For the case of the Burgers equation $$u_t + (u^2)_x = 0$$ the computation of N-wave solutions is in equation (2.1) of the paper

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057.

But I don't see how to extend this computation to the model above in the question.

How can we compute the "N-wave" source-solution of the conservation law $$u_t - u_x^2 + u_x = 0 \ ?$$

Note: For the case of the Burgers equation $$u_t + u_x^2 = 0$$ the computation is equation (2.1) in

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057,

but I don't see how to extend it to the model above.

How can we compute the "N-wave" source-solution of the conservation law $$u_t + (u - u^2)_x = 0 \ ?$$

Note: For the case of the Burgers equation $$u_t + (u^2)_x = 0$$ the computation of N-wave solutions is in equation (2.1) of the paper

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057.

But I don't see how to extend this computation to the model above in the question.

How can we compute the "N-wave" source-solution of the conservation law $$u_t - u_x^2 + u_x = 0 \ ?$$

Note: For the case of the Burgers equation $$u_t + u_x^2 = 0$$ the computation is in

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057.

(equation (2.1)), pdbut I don't see how to extend it to the model above.

How can we compute the "N-wave" source-solution of the conservation law $$u_t - u_x^2 + u_x = 0 \ ?$$

Note: For the case of the Burgers equation $$u_t + u_x^2 = 0$$ the computation is equation (2.1) in

Liu, Tai-Ping; Pierre, Michel, Source-solutions and asymptotic behavior in conservation laws, J. Differ. Equations 51, 419-441 (1984). ZBL0545.35057,

but I don't see how to extend it to the model above.